If you have to transfer your steam save games from one disk to an other disk check
out this website I found at forums.steampowered.com
Friday, December 25, 2009
Monday, December 14, 2009
Thursday, December 10, 2009
Monopoly Home Rules
These optional house rules may make Monopoly a whole new game for you. Please let me know if you have played any good home rules that I have not mentioned, or if you play with any of these rules tell me what you thought of them. I mark the ones I recommend.
Increase movement options:
Dice Choice
Rule: A player must roll two dice on his turn, but may select any two dice from a set of four sided, six sided, eight sided, and ten sided dice.
Reason: Gives players some control over movement. Players may wish to role two four sided dice at the beginning, since they have a better chance of getting doubles and going again, and then later roll two ten sided dice to move around the board quickly. Larger dice decrease the chance for doubles and thus tend to balance the game.Dice Control
Rule: A player may choose to roll only one die on his or her turn rather than two. If the player rolls a one, he or she must go directly to jail for making an “impossible” movement.
Variations: A player may announce before making a roll of two dice that he or she is going to move the product of the dice rather than the sum. If the player then rolls higher than twenty, the player is sent to jail for “speeding”, and as above if the player rolls a one, he or she must go directly to jail for making an “impossible” movement.
Reason: Gives players some control over movement. This rule is probably only a good idea if Maximum Punishment is in effect, otherwise players may use this rule to get into jail quickly.Traveling Railroads recommended
Rule: Whenever a player lands on a railroad, the player may choose to move his or her token to any other railroad owned by the same player.
Clarifications: The player must pay rent even if he or she does not travel. A player may travel on his or her own railroads, for free of course. A player may not travel on unowned railroads. Travel is across the board, so a player does not get $200 for passing Go when he or she travels from Short Line to Reading Railroad. The owner of the railroads may not prevent the player from traveling. A player may travel to or from a mortgaged railroad.
Variations: The owner may disallow a player from traveling on his or her railroads if the owner refuses to take the rent from the player landing on it. The owner must decide to disallow travel before the player is required to specify his or her destination, if any. The owner must allow travel from a mortgaged railroad.
Reason: Gives players control over their tokens, and makes the ownership of the railroads important. For example, The player developing the green properties should attempt to split up the railroads so that players landing on them do not always travel to Short Line and thus skip the green group. On the other hand, the player developing the dark blue group should encourage a railroad monopoly, since so many players move to Short Line to get closer to go and are more likely to land on the dark blue group.Increase development options:
Double Hotels
Rule: Players may build up to two hotels on a property. Rent must be paid on all buildings on a property.
Clarifications: After a player has raised a hotel on a property, he or she may purchase up to four more houses on that property and then may purchase a second hotel for that property. A player may not have more than four houses on a property.
Example: If a player has a hotel and two houses on Park Place and a hotel and three houses on Boardwalk, the rent is $2000 on Park Place and $3400 on Boardwalk.
Reason: Gives players more building options. Players may also more easily create a building shortage.Free Market
Rule: Players may build houses on any property they own, even if they do not have a complete set. If a player lands on a property which has been improved, they can either pay what they owner asks, up to a maximum of the normal amount required, or they may instead pay rent to any other owner of one of the other properties in the group, paying whatever rent that owner requests. If the player chooses to pay a different owner, including his or her own property in the group, then the player also moves his or her token to that property.
Clarifications: A player may not switch to a different property in the group if the property is not improved, nor may he or she switch to a property owned by the bank. If a player owns all of the properties in a group, he or she can charge the maximum rent allowed, and the player landing on his or her properties may not switch to a different property in the same group. When a player owns two properties in a three-property group, he or she must improve those two properties evenly. If a player acquires all the properties in a group, he or she must rectify the number of houses on each property so that the number of houses meet the even building rule.
Example: George owns Illinois and Kentucky Avenues, and Samantha owns Indiana Avenue. George decides to build three houses on each property, and Samantha decides to build just two on Indiana Avenue. Along comes Fred, who lands on Illinois. George asks him to pay the normal $750 rent for three houses. Naturally, he decides to switch his token to Samantha to pay her the $250 she is charging. George doesn’t want to lose money that he hoped would be his, so he offers to allow Fred to stay on Illinois for only $200. Samantha drops her rent to $200 as well, and points out that George is winning already and should not be given more money. Fred can accept either offer.
Reason: Makes the reason for owning a monopoly a much more clear goal.Instant Hotels
Rule: A player may purchase hotels for one of his or her monopolies at the cost of five houses, less any houses already owned, even if there are not enough houses for each property on the group to own four.
Reason: A housing shortage only hurts players who have little money. Players with a lot of money can go straight to hotels.Partnerships
Rule: Two or more players may agree to form a partnership with a property group in which they have a monopoly between them. Each partner may then purchase houses or hotels for the property they own as long as they follow rules for building evenly. A player may leave the partnership between dice rolls, forcing all players in the partnership to sell all of their buildings.
Example: Peter owns Boardwalk and Sarah owns Park Place. They agree to form a dark blues partnership and Peter builds a house on Boardwalk. Sarah later builds two houses on Park Place so Peter builds another two houses on Boardwalk. Players who land on Park Place are forced to pay $500 to Sarah and players who land on Boardwalk must pay $1400 rent to Peter. Sarah later lands on Board Walk and pays Peter $1400 in rent. In disgust she dissolves the partnership and sells her two houses on Park Place for $200. Peter must sell his three houses for $300.
Reason: Gives more options to players.Six Railroads recommended
Rule: The two utilities are treated like additional railroads. They cost $200 to buy and can be mortgaged for $100. The rent for five railroads is $300 and for six railroads is $400.
Reason: Makes the utilities actually worth having and a railroad tycoon a serious opponent.Uneven Building recommended
Rule: Once a monopoly is gained, the owner is allowed to build houses or hotels on the monopoly in any way he chooses.
Example: A player who owns both dark blue properties may purchase a hotel and place it on Boardwalk with no building on Park Place.
Reason: Allows players latitude to build as they choose and hope for a high rent gain without having to pay to improve the entire monopoly.Non-Monopoly Building recommended
Rule: You may build houses on properties for which you do not own all the properties of a set, but the houses cost double their normal price. If you sell them back to the bank, you still only get half of their normal cost.
Reason: Allows players to still build on properties without gaining the entire set, but at a cost.Unlimited Housing
Rule: There is no limit to the number of houses and hotels in the game.
Reason: Removes the possibility of a housing shortage, and allows players who have had difficulty getting together a monopoly until later in the game a chance to improve their properties.Flexible negotiations:
Immunity recommended
Rule: A player may grant full or partial immunity from paying rent on one or more of his or her properties as part of negotiations. The details of the immunity are up to the players involved in the trade.
Clarifications: Immunity does not transfer with the property if it is traded. A player who has granted immunity to another player and then trades the property away and then later trades to get it back still must honor the original immunity given.
Example: In a six player game, George owns three railroads and Illinois, and Lisa owns the fourth railroad and the other two red properties. Lisa agrees to give the fourth railroad to George and allow him two free visits on the red group whenever he chooses. In exchange, George gives Lisa Illinois and immunity from paying rent on his railroads for the entire game. Later in the game, although George has been collecting $200 from the other four players fairly frequently, and used his free visits to avoid paying rent on Kentucky with three houses and later Illinois with a hotel, he is bankrupted from landing on Edgar’s New York Avenue hotel. Edgar thus acquires the railroads and Lisa must now pay rent to Edgar’s railroads when she lands on them.
Reason: Gives more options when negotiating trades.Loans recommended
Rule: A player may loan another player money or property at any agreed upon rate or with any agreed upon provisions.
Reason: Removes a restriction imposed by the original rules.Profit Sharing recommended
Rule: Two or more players may agree to split the rent from a property or set of properties.
Clarifications: Like Immunity, Profit Sharing does not transfer with the property if it is traded. A player who has granted profit sharing to another player and then trades the property away and then later trades to get it back still must honor the original profit sharing plan.
Example: In a six player game, Norman owns two railroads and Gary owns two railroads. Norman agrees to sell his two railroads to Gary for $400 and Gary promises to give Norman $100 of each $200 he collects in rent from the railroads.
Reason: Gives more options when negotiating trades.Balance the game:
Bank Repossession recommended
Rule: When a player is bankrupted by debts to another player, the debtor must mortgage all his or her properties, pay the creditor as much as possible, and then return all of the debtor’s properties to the bank. These properties are then available for purchase by other players as usual.
Clarifications: As with the normal rules, the debtor may not sell or trade any of his or her properties unless it gives enough money to pay the debt. The original rules also state that property acquired by the bank due to a player becoming bankrupted must be auctioned off immediately, but in this rule, this auction does not occur, and players must land on the properties in question to be able to purchase them.
Reason: Often when one player is winning and they bankrupt another player, that player gains enough property and money to insure winning the game. This rule makes the end of the game have all of the interest of the beginning, since a bankruptcy floods the board with new properties to be purchased.Double Prices recommended
Rule: All property costs twice the face value.
Clarifications: Mortgage values remain the same, as do all other values.
Variations: If the player landing on the property does not end up buying it, he or she gets a “finder’s fee” of %10 of the sale cost.
Reason: Property is too inexpensive. In the normal game, it is always a good strategy to purchase property because even if it is not part of a monopoly that one owns, it can be traded for something more useful or mortgaged if not. As a result of this rule, players usually put property up for auction unless they really want it. This rule makes the game much more challenging, since players actually must think about what they are willing to buy and when to start an auction.Maximum Punishment recommended
Rule: A player in Jail may not collect rent, buy buildings, participate in any auctions, or mortgage property. He or she may only make trades with another player in Jail or any player at Just Visiting.
Variations: A player may pay $100 immediately upon reaching jail to be placed in Just Visiting, and thus avoid a turn in jail. Good lawyers are expensive.
Reason: Makes jail a punishment rather than a safe haven.Option to Auction
Rule: Whenever a player lands on an unpurchased property, any other player can immediately start an auction for that property by bidding twice the normal purchase price.
Reason: Balances bad dice rolls by allowing players who are willing to pay extra for particular properties to have a chance at them.Initial Auction
Rule: Before the game begins, everyone writes down how much they will pay for every property on the board in a closed auction. This can be done independently, before even gathering to play. The game then begins by checking everyone’s bids and selling the properties to the highest bidder for each property, with ties broken by die roll. In this variation, start the game with more money: $10,000 divided by the number of players should be about right.
Reason: This makes the purchase of property much more interesting, removing the luck element and moving the beginning of the game along much faster, ending up quickly in the property negotiations and house purchasing. As a result, the entire game is about interesting choices, not about waiting for players to get lucky or unlucky with property purchases.Tax Man
Rule: The bank gets a token known at the “tax man” and a player will roll the dice for the bank on it’s turn. If it lands on any owned property, the owner pays the bank the amount that would normally be charged in rent. The tax man ignores the normal meaning of any other square, including “Go to Jail”.
Reason: Balances the benefit of a property that often gets landed on due to it’s placement on the board.Facilitate the game:
Honest Game recommended
Rule: Players must always pay rent, even if the owner does not ask.
Reason: Removes the annoying requirement of constantly have to watch where other players land. Also allows a game to be more social as players can trust each other to pay rent when required.Closed Auction recommended
Rule: All auctions are done by players writing down a bid and then showing in unison.
Reason: Open auctions with players yelling out bids is chaotic and tedious.Minimum Bid
Rule: Any new bid in an open auction must be at least $10 more than the previous bid.
Reason: Cuts down on tedious $1 raise auctions.Sudden Death
Rule: Before the game begins, one player is secretly and randomly determined to be the “Angel of Death”. This can be done by having one slip of paper put into a hat for each player, with a star on one of them, and then each player draws a slip. The Angel of Death player has the option, once the game has been played for two hours, of smashing the board and declaring the game over without any winner. The Angel of Death may only do so if he or she is still in the game.
Reason: The game moves much faster as players fight against time, and may end before it really drags out.Allow many players:
Double Board
Rule: Two boards, such as a standard board and an English board, have either Free Parking or Go overlapping. Players go around both boards in a figure eight pattern. When a player lands on the overlapping space, he or she may choose which board to enter next. When a player is sent to jail, he or she is sent to the jail on the board that they were occupying before going to jail.
Clarifications: A player advancing to a named property as per instructions on a card may pass Go twice, collecting $400.
Variations: Cards which affect all players or all properties, such as “pay all players $50″ or “building repairs”, only affect the properties and the players on the same board as the affected player.
Reason: Useful for games with more than five players to allow for more possible monopolies.First to Go
Rule: Players may not purchase properties until one player has passed Go.
Reason: In games with lots of players, going first gives a great advantage toward acquiring property, and going last is a major hinderance. If players can not start to purchase property until they are spread around the board, then this disparity is smaller.Order Auction
Rule: Before the game begins, players bid for the right to go first. The order of play is based upon the amount of money bid.
Reason: In games with lots of players, going first gives a great advantage toward acquiring property, and going last is a major hinderance. By paying for the privilege, the games is more fair.Start at Corners recommended
Rule: Players put their tokens at the four corners of the board rather than Go as their starting positions. The player on “Go to Jail” does not. Players should be spread evenly to all the corners, and which player starts at which corner should be determined randomly.
Reason: By starting in different locations, the players are less likely to land on properties already owned by players who went before them.Increase money supply:
Bank Loans
Rule: a player without an outstanding loan may at any time take out a $500 loan from the bank. Every time the player passes Go he or she only receives $100, the other $100 remaining in the bank as interest. The loan may be repaid any time after the player has passed Go and given the bank interest at least once.
Clarifications: If a player bankrupts the debtor, he or she inherits that debt, unless the “Bank Repossession” rule is used, in which case the bank dissolves the debt.
Reason: Gives players more monetary options.Double Salary
Rule: A player who lands on Go gets $400 rather than $200.
Clarifications: Players who pass Go only get the usual $200.
Reason: Puts more money into the game to make it easier.Free Parking Jackpot
Rule: $500 is placed in the middle of the board at the start of the game. Any time a player must pay a fine or tax the money also is put in the middle of the board. Whenever a player lands on Free Parking, he or she gets the money in the middle.
Clarifications: The $500 is not replaced after the jackpot is first taken. It is only for the first lucky player to land there.
Variations: Play without the $500 jackpot, or with only $50 which is replaced every time a player lands there. Some players only put Luxury Tax money there. Note: This is the most common home rule that people play, and there are lots of variations on it. Some have more money, some have less, but there are so many ways it is done, I can’t list them all.
Reason: Throws another variable into the game and gives a losing player a chance to get back into the game, or at least a dim hope.Miscellaneous:
Doubling Up
Rule: Only one token may be on a square at a time, except on Go and Jail. When a player’s token lands on a space already occupied by another player, the player moves his or her token backwards to Go and his or her turn is over. No money is collected for moving backwards to Go.
Reason: Has the effect of lowering the amount of money in the game because players pass Go less often, and the lower valued properties are landed on more frequently.Foreclosure
Rule: When a player lands on a mortgaged property, the owner may immediately unmortgage the property by paying the mortgage value plus %10 interest. If the owner does not do this, the player may purchase it by paying the player the mortgage value and the bank the mortgage value plus the %10 interest. Either way the player still pays no rent.
Reason: Makes mortgaging property more difficult and more dangerous.No Mortgaging recommended
Rule: You cannot mortgage property. You are allowed to sell property back for half the printed purchase price.
Reason: Mortgaged property makes the game much less interesting. By removing that option from players, they must make hard decisions. Further, interesting properties may reappear on the board for sale. Often players may decide to have their own auction for a property instead of selling it back to the bank.Optional Draw
Rule: When a player lands on Chance or Community Chest, drawing a card is optional.
Reason: Gives more options and control.Two Tokens
Rule: Each player has two tokens, and alternates which token is moved each turn.
Reason: In a two player game, this means that both players have tokens covering more space on the board. This is particularly interesting when making house buying decisions, because one of your opponent’s tokens may have passed your monopoly, but the other may be coming up to it, thus a house purchase may be a good idea. With just one token, you know how far the opponent is from your monopoly, and the decisions are not as interesting.
Tuesday, December 1, 2009
Wednesday, November 25, 2009
Saturday, November 21, 2009
Saturday, November 14, 2009
Dumb things to check (from whatexit.org)
a list of dumb things to check
found at whatexit.org
- Is the filename extention right? Should it be .php instead of .html?
- You can get to the web site? Are you working in "off-line" mode?
- Make sure CapsLock is off. (Same for ScrollLock and NumLock)
- Is there a (invisible) CTRL-M at the end of each line in the text file?
- Does the text file end with a newline?
- Are both ends of the (power/network/video/etc.) cable plugged in?
- Did you unplug and re-plug in the cable to make sure its in right?
- Is the cable plugged into the right jack? (Some jacks look the same: AUI and video, Some Sun's have a 'stealth' video jack that you aren't supposed to use, etc.)
- "Did you get permission to run crack against that password file?" ... "Is it in writing?"
- Is the user pressing RETURN when you think they are? (Are they pressing it at all?)
- Is the user typing a "/" or a "\"?
- Does the user know which is the lessthan and which is the greaterthan symbol?
- Is the screen paused via Ctrl-S? (press CTRL-Q to find out)
- Does your test gear test what you think it tests? What happens when you run the exact same test on a known-good and a known-bad element? Do you get the results you expect both ways?
- Does plugging a lamp into that outlet make it light up? (If you use a radio, be careful of radios with battery backups)
- Is the laptop running off battery? (therefore obscuring a power problem)
- Use cut-and-paste to copy that variable name (or URL, commmand line, etc.) to see if it was entered correctly.
- Check the file permissions.
- Check the environment variables (Use "strings" on the binary to find out what they really are supposed to be).
- It's too easy to answer "yes" when asked, "Is it plugged in." It's better to ask them to power it off, then power it back on OR ask them to "check both ends of the power cable" OR ask them if the power light is on, off, or blinking. (and if it's blinking... RUN!)
- Type it again (without using cut-and-paste) and see if you get the same results. (good way to find a typo)
- Is the default route set? Is the netmask set correctly?
- Traceroute from A to B. Traceroute B to A. Do they match up?
- Is someone else also at that IP address? (Unplug the network cable and ping the address)
- Are you really on the host you think you are?
- Is the program reading the last line of the file? Is it being processed right?
- Are you doing the test from the right machine? Would the test be more effective from a different machine?
- (firewall ruleset issues) If you move the machine to another IP address does it still happen? If you move the machine to a different subnet does it still happen? If you put a different machine at that IP address does it still happen? If you boot the same machine on a different OS (like a CD-ROM based Linux or FreeBSD) does it still happen?
- Does the same thing happen when you specify the IP address instead of the hostname? (Hint: the lmhost or /etc/hosts may be overriding)
- Is that a file, a directory, a hard link, a symbolic link, or a mountpoint?
- http://www.psc.edu/~mathis/MTU/index.html: Six classes of bugs limit network performance.
- packet losses, corruption, congestion, bad hardware
- IP Routing, long round trip times
- Packet reordering
- Inappropriate buffer space
- Inappropriate packet sizes
- Inefficient applications
- Are the binaries really the ones you think are running? (Did you install in single user mode when /opt wasn't mounted? Can you check the md5 or sha1 checksum vs. a machine that is running properly?)
- Is DNS configured right? Misconfigured DNS masks other problems and appears as bizarre problems that will send you looking everywhere except /etc/resolv.conf
- Is there a rogue DHCP server on the network messing with you?
- Is the device driver you're trying to install for the device you actually have?
- Did you remember to check this list?
Friday, November 13, 2009
Comet Hunter’s Last Look at Earth Is Haunting
This gorgeous image of a blue arc of the Earth against the blackness of space was captured by the Rosetta spacecraft as it swung by our planet.
The European Space Agency mission is on its way to intercept the comet, 67P/Churyumov-Gerasimenko. The ship will deploy a lander onto the comet’s surface, the first such attempt to be made.
To gather up the necessary energy to reach the comet out past Mars’ orbit, Rosetta needed three swings past Earth. This is its third and final flyby. It will reach the comet in early 2014.
Unlike the most famous pictures of Earth, which show most of the blue marble, this photo presents a planet in darkness, just the South Pole awash in light.
Image: ESA. High-resolution image of planet Earth from Rosetta.
See Also:
- Out of the Blue: Islands Seen From Space
- Stunning Views of Glaciers Seen From Space
- Asteroid Impact Craters on Earth as Seen From Space
- Erupting Volcanoes on Earth as Seen From Space
- First-Ever Asteroid Tracked From Space to Earth
- Time-Series Photos From Space of Aral Sea Death
WiSci 2.0: Alexis Madrigal’s Twitter, Google Reader feed, and green tech history research site; Wired Science on Twitter and Facebook.
via feeds.wired.com
Wednesday, November 11, 2009
Monday, November 9, 2009
codinghorror.com; Whitespace: The Silent Killer
So true it's scary via codinghorror.com
Whitespace: The Silent Killer
Ever have one of those days where everything you check into source control is wrong?
Also, how exactly is that day is different from any other? But seriously.
Code that is visible is code that can be wrong. No surprise there. But did you know that even the code you can't see may be wrong, too?
These are the questions that drive young programmers to madness. Take this perfectly innocent code, for example.
Looks fine, doesn't it? But hold on. Wait a second. Let's take another, closer look.
OH. MY. GOD!
If you're not a programmer, you may be looking at these two images and wondering what the big deal is. That's fine. But I humbly submit that, well, you're not one of us. You don't appreciate what it's like to spend every freaking minute of every freaking day agonizing over the tiniest details of the programs you write. Not because we want to, you understand, but because the world explodes when we don't.
I mean that literally. Well, almost. If one semicolon is out of place, everything goes sideways. That's how programming works. It's fun! Sometimes! I swear!
We got into this industry because, quite frankly, we are control freaks. It's who we are. It's what we do. Now to imagine, to our dismay, that there's all this stupid, useless whitespace at the ends of our lines. Stuff that's there, but we can't see it. Well, those are the nightmares OCD horror movies are made of. I have a full-body itchiness just talking about it.
Depending on how far down the rabbit-hole you want to go, there's any number of things you could do here:
- Have a post-build step, perhaps something with a regular expression like
\s*?$in it, that auto-cleans extra spaces checked into source control- Execute a local macro which removes whitespace from ends of lines
- Have a special rule to highlight extra spaces
- Run your IDE in whitespace-always-visible mode, or toggle it frequently
OK, fine, so maybe the world won't explode if there are a few extra bits of whitespace in my code.
But all the same, I think I'll go back and make extra double plus sure no more of that pesky whitespace has accumulated in my code when I wasn't looking. Just because I can't see it doesn't mean it's not out to get me.
[advertisement] JIRA 4 - Simplify issue tracking for everyone involved. Get started from $10 for 10 users.
Posted by Jeff Atwood View blog reactions
Thursday, October 29, 2009
Tuesday, October 27, 2009
Monday, October 26, 2009
How to Upgrade to Windows 7 Retail from the Beta or Release Candidate [Windows 7]
Nuttige info als je aan de Beta of RC wenst te upgrade, natuurlijk het zou beter zijn als zij (MS) kon doen wat in de Linux wereld normaal is en gewoon in een package manager upgraden met een paar klikjes van de muis ;-)
Hello, early adopter—your eyes might've glazed over during the Windows 7 launch because you've been on that train for months now. This is for you: how to upgrade that Windows 7 release candidate to a final version, easy.
Basically, copy of all of the files from the retail disc to a folder on your hard drive, pop open the "sources" directory in that folder, and open up the file called "cversion.ini" in Notepad. Change the number 7233 to read 7000 (you're telling it the minimum version that's allowed to upgrade). Save it, and now you can do an upgrade install. You might see some slight wonkiness, but Max PC says they've had some "good results" this way. [Maximum PC]
Send an email to matt buchanan, the author of this post, at matt@gizmodo.com.
via feeds.gawker.com
Sunday, October 25, 2009
Tuesday, October 20, 2009
Tuesday, October 13, 2009
Friday, October 9, 2009
Wednesday, October 7, 2009
Saturday, October 3, 2009
Monday, September 28, 2009
Sunday, September 27, 2009
How many trig functions are there? — The Endeavour
How many trig functions are there?
by John on September 25, 2009
How many basic trigonometric functions are there? I will present the arguments for 1, 3, 6, and at least 12.
The calculator answer: 3
A typical calculator has three trig functions if it has any: sine, cosine, and tangent. The other three that you may see — cosecant, secant, and cotangent — are the reciprocals of sine, cosine, and tangent respectively. Calculator designers expect you to push the cosine key followed by the reciprocal key if you want a secant, for example.
The calculus textbook answer: 6
The most popular answer to the number of basic trig functions may be six. Unlike calculator designers, calculus textbook authors find the cosecant, secant, and cotangent functions sufficiently useful to justify their inclusion as first-class trig functions.
The historical answer: At least 12
There are at least six more trigonometric functions that at one time were considered worth naming. These are versine, haversine, coversine, hacoversine, exsecant, and excosecant. All of these can be expressed simply in terms of more familiar trig functions. For example, versine(θ) = 2 sin2(θ/2) = 1 – cos(θ) and exsecant(θ) = sec(θ) – 1.
Why so many functions? One of the primary applications of trigonometry historically was navigation, and certain commonly used navigational formulas are stated most simply in terms of these archaic function names. For example, the law of haversines. Modern readers might ask why not just simplify everything down to sines and cosines. But when you’re calculating by hand using tables, every named function takes appreciable effort to evaluate. If a table simply combines two common operations into one function, it may be worthwhile.
These function names have a simple pattern. The “ha-” prefix means “half,” just as in “ha’penny.” The “ex-” prefix means “subtract 1.” The “co-” prefix means what it always means. (More on that below.) The “ver-” prefix means 1 minus the co-function.
Pointless exercise: How many distinct functions could you come up with using every combination of prefixes? The order of prefixes might matter in some cases but not in others.
The minimalist answer: 1
The opposite of the historical answer would be the minimalist answer. We don’t need secants, cosecants, and cotangents because they’re just reciprocals of sines, cosines, and tangents. And we don’t even need tangent because tan(θ) = sin(θ)/cos(θ). So we’re down to sine and cosine, but then we don’t really need cosine because cos(θ) = sin(π/2 – θ).
Not many people remember that the “co” in cosine means “complement.” The cosine of an angle θ is the sine of the complementary angle π/2 – θ. The same relationship holds for secant and cosecant, tangent and cotangent, and even versine and coversine.
By the way, understanding this complementary relationship makes calculus rules easier to remember. Let foo(θ) be a function whose derivative is bar(θ). Then the chain rule says that the derivative of foo(π/2 – θ) is -bar(π/2 – θ). In other words, if the derivative of foo is bar, the derivative of cofoo is negative cobar. Substitute your favorite trig function for “foo.” Note also that the “co-” function of a “co-” function is the original function. For example, co-cosine is sine.
The consultant answer: It depends
The number of trig functions you want to name depends on your application. From a theoretical view point, there’s only one trig function: all trig functions are simple variations on sine. But from a practical view point, it’s worthwhile to create names like tan(θ) for the function sin(θ)/sin(π/2 – θ). And if you’re a navigator crossing an ocean with books of trig tables and no calculator, it’s worthwhile working with haversines etc.
Related posts:
Mercator projection
Why care about spherical trig?
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Connecting trig and hyperbolic functions without complex numbers
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The story of the Gömböc
The story of the Gömböc
by Marianne Freiberger
Play this movie to see the Gömböc wriggle. This article is also available as a podcast.
A Gömböc is a strange thing. It looks like an egg with sharp edges, and when you put it down it starts wriggling and rolling around with an apparent will of its own. Until quite recently, no-one knew whether Gömböcs even existed. Even now, Gábor Domokos, one of their discoverers, reckons that in some sense they barely exists at all. So what are Gömböcs and what makes them special?
Balancing act
The defining feature of a Gömböc is the fact that it's got just two points of equilibrium: one is stable and the other is unstable. If you put a Gömböc down on a flat surface, resting on its stable equilibrium point, it will stay as it is. "Even if you kick it a little, it will come back to its resting position at the stable equilibrium point," says Domokos, a mathematician at Budapest University of Technology and Economics. "The other equilibrium point is unstable. You can balance the Gömböc at this point a bit like you can balance a pencil on its tip: the slightest push will make it fall over." It's impossible to balance a Gömböc on any other point: if you try, it will move off in a specific direction. That's why the Gömböc seems to have a life on its own: put it down at a non-equilibrium point, and it will start rolling around in a systematic way until it has reached the stable equilibrium position. In other words, the Gömböc is self-righting.
A Gömböc made from plexiglass.
"It's a bit like putting a ball on a hilly landscape," says Domokos, "if you put the ball down at a generic point, it will always roll off in the same direction, down into the valley. If you put it on a hill top, it will also roll off, but the direction depends on the direction in which you kick it — that's the unstable equilibrium. Put it in the valley, and it will not roll off at all — that's the stable point of equilibrium."
To give it its full mathematical description, a Gömböc is a three-dimensional, convex and homogeneous object with exactly one stable point of equilibrium and one unstable point of equilibrium. Requiring it to be homogeneous amounts to saying that you're not allowed to cheat: the material from which the Gömböc is made has to be uniform throughout, so you're not allowed to use weights, as those found in roly-poly toys, or other irregularities to get the Gömböc to self-right. Convexity means that the Gömböc is not allowed to bulge inwards, in other words, the straight line connecting any two points on the Gömböc has to lie entirely within the Gömböc. It's easy to create a non-convex shape with one stable and one unstable equilibrium point, hence the restriction to convexity.
Doubtful existence
An ellipse has two stable and two unstable points of equilibrium.
The reason why many people thought that Gömböcs didn't exist is that in two dimensions there is no convex shape with only two points of equilibrium. "Imagine you have a shape made from plywood," says Domokos, "which is moving between two vertical glass plates. Then the shape would balance at some points. An ellipse, for example, would balance at the centres of its two 'long sides' — these are the stable equilibrium points — and at the centres of its two 'short sides', these are the unstable points." A square can balance on the centres of its four sides, the stable equilibria, as well as on each of the four vertices, though rather precariously, making the vertices unstable equilibria. Similarly, an n-sided polygon has n stable equilibrium points — the centres of its sides — and n unstable ones — its vertices.
It turns out that two stable and two unstable equilibrium points is the best you can do in two dimensions, and it's relatively easy to prove this. The proof basically amounts to showing that a convex shape with just one stable and one unstable equilibrium point makes impossible demands on its centre of gravity (see here for some more detail).
Many mathematicians, including Domokos, concluded that the same result should hold in three dimensions, and they set out to prove it. "The fact that no-one could imagine a three-dimensional shape with just one pair of equilibrium points suggested that it would be worth-while to disprove its existence," he explains. "I tried to do this, unsuccessfully, for a very long time. Then I had a conversation with [the Russian mathematician] Vladimir Arnold, in which he expressed the view that such a shape might exist after all, despite all the rumors going around that it didn't. This made me think in a different way, and I soon realised that the problem was much more beautiful than I had thought at first."
A geometric stem cell
The beautiful fact that Domokos discovered, with the help of his colleague Peter Várkonyi, was that a Gömböc, if it existed, would be a sort of stem cell from which you could "grow" three-dimensional shapes with all other configurations of equilibrium points.
If you balance a marble at a saddle point, the balancing act is stable in one direction and unstable in infinitely many other directions.
In three dimensions, stable and unstable points are not the only equilibrium points: you can also have saddle points. If your object is balanced on a saddle point, then the balancing act is unstable in infinitely many directions — if you push your object in any of these directions it will topple over — and stable in exactly one direction — if you give it a slight push in that direction, it will come back to the equilibrium point. This is similar to a marble balancing on the mid-point of a saddle. You can make it roll down the sides of the saddle in infinitely many directions, but if you push it exactly along the line running from the front to the back of the saddle, something that's admittedly quite hard to do, it will roll back to the saddle point.
For a convex and homogeneous three-dimensional object, the number of saddle points depends on the number of stable and unstable equilibria: if the object has i stable and j unstable equilibria, then it has i+j-2 saddle points. You can prove this fact mathematically, and it's known as the Poincaré-Hopf theorem. Inspired by this nice relationship, Domokos set out to classify three-dimensional shapes according to their number and type of stable and unstable equilibrium points: given numbers i and j, which objects, if any, have i stable and j unstable points of equilibrium (and therefore i+j-2 saddle points)?
"It was not known if there were objects for each category [formed by an (i,j) pair]," says Domokos. "But we did have some examples. The cube, for example has six stable points of equilibrium [the centres of the six faces], eight unstable points [the eight vertices], and twelve saddles [the centres of the twelve sides]. We also knew about the tetrahedron and many other objects, but there are infinitely many categories. Then we realised that it is always possible to increase the number of equilibrium points by one using a small perturbation." In other words, a small but purposeful deformation of the object would give rise to one extra equilibrium point.
"This is intuitively clear," says Domokos. "If you go on a hike and need to collect some water, then you can dig a small hole, and water will collect in that hole. So with a very small perturbation you have produced a stable point of equilibrium. However, the opposite is not true: getting rid of a lake [which contains a stable equilibrium point] is no easy job. Similarly, if you have an object, it is generally not easy to get rid of an equilibrium point, but it is possible to create one." Domokos and Várkonyi found an explicit algorithm telling you exactly how to endow a convex and homogeneous three-dimensional shape with an extra equilibrium point.
This result was momentous as far as the not-yet-discovered Gömböc was concerned. "It told us that if you had an object [with the minimal number of equilibrium points, one stable and one unstable], then this would prove that objects exists in all other classes too, because you can increase the number of equilibrium points one by one. So this object would be like a stem cell: you could derive the existence of all other categories from it, but you couldn't derive its existence from bodies with higher numbers of equilibrium points. Mathematics is all about beauty, and this result is very beautiful."
Mathematical field work
Pebbles from beaches on the island of Rhodes. The left pile contains convex pebbles and the right pile contains concave pebbles.
But despite this tantalising beauty, Domokos and Várkonyi's attempts to prove the Gömböc's existence remained futile, so Domokos took a desperate measure. On a holiday to a Greek island he and his wife collected and inspected 2000 beach pebbles in the hope that they might find one behaving like a Gömböc. It was a strenuous effort, which a weaker relationship may not have survived, and it failed. "We learned very interesting things from a pebble point of view, but nothing from a Gömböc point of view," says Domokos. "We were tired and depressed. When you looked at these pebbles you got the feeling that even if you went to all other Greek islands, you would never find [one behaving like a Gömböc]. But why not? If this type of pebble doesn't exist, then there must be a mathematical reason for this."
This line of thought led to an important insight into the Gömböc's nature: Domokos and Várkonyi realised that a Gömböc, if it existed, could not be very flat, or very thin. A flat object, like a frisbee, generally has two sides, and contained in each there'll be a stable equilibrium point — that's one stable equilibrium too many for a Gömböc. A thin object, like a pencil, will generally have two unstable equilibrium points at its two tips, so it cannot be a Gömböc either.
The perfect figure
Thin objects like this pencil generally have two unstable points of equilibrium at their tips, while flat objects, like these pebbles, generally have two stable points of equilibrium.
Domokos and Várkonyi made their intuition precise by giving a formal mathematical definition of what they meant by flatness and thinness, each measured by a number greater than or equal to 1. They then proved that a Gömböc's flatness and thinness both have to be equal to 1, that is, both values have to be as small as is possible.
The result gives some insight into why the Gömböc is only just teetering on the brink of existence. If you make a Gömböc just a tiny little bit thinner or flatter, then its flatness and thinness values aren't minimal anymore. So according to the result, the object stops being a Gömböc — it must have gained extra equilibrium points, or stopped being convex.
The Gömböc's sensitivity to change means that a Gömböc-like pebble can only exist for a short time on the sea shore before other pebbles, moved by the sea, start chipping away its Gömböc-ness and turn it into an ordinary pebble. "It's a fundamental question," says Domokos, "to which you expect a clear-cut answer: something should either exist or not exist. But in the case of the Gömböc, the answer is that it does exist, but barely so. If you drop it, it ceases to be what it was, so physically, it is a very fragile existence."
Finally, a Gömböc!
Having thus explained why they had not been able to find a Gömböc on the beach, Domokos and Várkonyi drew new hope and tried a new line of attack in their search for a proof of its existence. In two dimensions a Gömböc is impossible because it needs a balancing that would require the centre of gravity of the shape to be in two places at once. But in three dimensions there is more space to balance things out, so Domokos and Várkonyi started tinkering around with various shapes until they had a description of an object with all the required Gömböc properties.
Many mathematicians would have stopped there — if you can prove that something exists, then why go on to build it? — but Domokos and Várkonyi wanted their very own Gömböc to take home. This proved difficult, as their initial construction was too close to an actual sphere. "The deviation from the sphere was only 10-5," says Domokos, "so with [a diameter of 1m], the object would differ from a sphere by a only hundredth of a millimeter." This surpasses the precision of even the most sophisticated tools. If you try to manufacture such a Gömböc, all you'll ever get is to all intents and purposes an ordinary sphere.
The problem was that Domokos and Várkonyi had wanted their object to be as smooth as possible, avoiding sharp edges as far as they could. It was only when they let this requirement go that they came up with a new and buildable version of a Gömböc. That's the version you can see in the pictures — note the sharp edges. But even this buildable version requires an incredible level of precision: the Gömböcs are now being manufactured using computer controlled machining with precision tolerances below 10 microns — that's about a tenth of the thickness of a human hair!
Gömböcs in nature
Play this movie to see a tortoise behaving like a Gömböc While the Gömböc made a good job of hiding from mathematicians, it didn't escape the penetrating gaze of evolution. Thinking that Gömböc-like shapes must appear somewhere in nature, Domokos turned his attention to tortoises. Being turned on its back is a potential disaster for any tortoise, so much so that the males in some species try to turn over their rivals during their battles for females. So any tortoise that's able to struggle back on its belly has an evolutionary advantage. Some species of tortoise manage to turn themselves back over using their muscular necks as a lever, while many others can't self-right at all.
Domokos started an extensive search in pet shops and zoos, turning over tortoises while their owners weren't looking, and finally found what he wanted: "Suddenly one day I came across the first little tortoise that was doing exactly what it was supposed to do," he recalls, "it was acting like a Gömböc!" The shell of this high-domed species is similar to a Gömböc — it contains no stable equilibrium point, so when an individual is put on its back, it automatically flips over into the only stable position: lying on its belly. Domokos conducted an extensive study of tortoises using a complex three-dimensional model of their shell, and identified two species, the Indian star tortoise and the radiated tortoise, which use their Gömböc-like shells to self-right. The results of his research were eventually published in the biological journal Proceedings of the Royal Society B in a paper co-authored by Várkonyi, and biologists have accepted that the Gömböc-like shells are indeed a result of natural selection in favour of the ability to self-right.
The Gömböc adventure has led Domokos to look deeper into the evolution of shapes in general. He's currently developing ways of deducing the habitat of a tortoise from the shape of its shell, a project that will enable scientists to learn more about the living spaces of extinct tortoises, of which only fossilised shells remain. He's also developed a model which explains how asteroids, that aren't round like planets, but have sharp edges and flat areas, evolve their shapes (the paper has been published in The Astrophyiscal Journal).
So the Gömböc, which started out as a question in the mind of a mathematician, not only exists in the abstract, but also in nature. And who knows what lies ahead of it in terms of human-made applications? For the moment, though, the Gömböc is being produced for purely aesthetic reasons, and enthusiasts can purchase their very own model on the Gömböc website. And if you find yourself close to Cambridge, you can come and admire a real Gömböc at the Whipple Museum of the History of Science, to which it was donated by Domokos and Várkonyi in April this year.
For a more technical look at the topics covered here read Domokos and Várkonyi's articles Mono-monostatic bodies: The answer to Arnold’s question and Static equilibria of rigid bodies: dice, pebbles, and the Poincaré-Hopf theorem . To hear Domokos himself speak about the Gömböc, listen to the podcast accompanying this article.
mechanics geometry equilibrium gömböc astronomy physics tiling relativity symmetry computer graphicsAbout this article
Gábor Domokos
Péter Varkonyi
Marianne Freiberger, Co-Editor of Plus, interviewed Gábor Domokos in Cambridge in May 2009.
via plus.maths.org
Monday, September 21, 2009
Battle of the buzzwords: Apple vs. Microsoft - Apple 2.0 - Fortune Brainstorm Tech
Apple vs. Microsoft
The Buzzwords
Elephant On Trampoline
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Dingen die ik me dan afvraag:
- Werd de slurf, staart en oren geanimeerd(manueel door mens) of gesimuleerd(automatich door software)
- Hoe lang duurde het om een gemiddeld beeldje te renderen
- Om dit in het echt te kunnen doen hoe sterk zou de trampoline moeten zijn, welke materialen zijn nodig
Sunday, September 20, 2009
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Charles Darwin film 'too controversial for religious America' - Telegraph
By Anita Singh, Showbusiness Editor
Published: 4:53PM BST 11 Sep 2009
Paul Bettany plays Charles Darwin in Creation Photo: ALLSTARCreation, starring Paul Bettany, details Darwin's "struggle between faith and reason" as he wrote On The Origin of Species. It depicts him as a man who loses faith in God following the death of his beloved 10-year-old daughter, Annie.
The film was chosen to open the Toronto Film Festival and has its British premiere on Sunday. It has been sold in almost every territory around the world, from Australia to Scandinavia.
However, US distributors have resolutely passed on a film which will prove hugely divisive in a country where, according to a Gallup poll conducted in February, only 39 per cent of Americans believe in the theory of evolution.
Movieguide.org, an influential site which reviews films from a Christian perspective, described Darwin as the father of eugenics and denounced him as "a racist, a bigot and an 1800s naturalist whose legacy is mass murder". His "half-baked theory" directly influenced Adolf Hitler and led to "atrocities, crimes against humanity, cloning and genetic engineering", the site stated.
The film has sparked fierce debate on US Christian websites, with a typical comment dismissing evolution as "a silly theory with a serious lack of evidence to support it despite over a century of trying".
Jeremy Thomas, the Oscar-winning producer of Creation, said he was astonished that such attitudes exist 150 years after On The Origin of Species was published.
"That's what we're up against. In 2009. It's amazing," he said.
"The film has no distributor in America. It has got a deal everywhere else in the world but in the US, and it's because of what the film is about. People have been saying this is the best film they've seen all year, yet nobody in the US has picked it up.
"It is unbelievable to us that this is still a really hot potato in America. There's still a great belief that He made the world in six days. It's quite difficult for we in the UK to imagine religion in America. We live in a country which is no longer so religious. But in the US, outside of New York and LA, religion rules.
"Charles Darwin is, I suppose, the hero of the film. But we tried to make the film in a very even-handed way. Darwin wasn't saying 'kill all religion', he never said such a thing, but he is a totem for people."
Creation was developed by BBC Films and the UK Film Council, and stars Bettany's real-life wife Jennifer Connelly as Darwin's deeply religious wife, Emma. It is based on the book, Annie's Box, by Darwin's great-great-grandson, Randal Keynes, and portrays the naturalist as a family man tormented by the death in 1851 of Annie, his favourite child. She is played in the film by 10-year-old newcomer Martha West, the daughter of The Wire star Dominic West.
Early reviews have raved about the film. The Hollywood Reporter said: "It would be a great shame if those with religious convictions spurned the film out of hand as they will find it even-handed and wise."
Mr Thomas, whose previous films include The Last Emperor and Merry Christmas Mr Lawrence, said he hoped the reviews would help to secure a distributor. In the UK, special screenings have been set up for Christian groups.
via telegraph.co.uk
Welcome to the FOOKUNITY
Biggest (and best) Fallout 3 mod arround and an example why PC gaming still beats console gaming. 
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Friday, September 11, 2009
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