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Four color theorem
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The Four Color Theorem is a famous mathematical theorem that states that no more than four colors are required to color the regions of any map so that no two adjacent regions have the same color. Adjacent means that two regions share a common boundary curve segment, not merely a corner where three or more regions meet. Unlike other proofs before its discovery, computers were used to resolve this long-standing mathematical conjecture that was first proposed in 1850 by Francis Guthrie. After more than a century later, mathematicians, Kenneth Appel and Wolfgang Haken, finally derived its proof in 1976, and determined that it is practicality impossible for humans to verify it without the use of a computer. According to the four color theorem, a ...
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5296 |
bio_man |
2 years ago |
Can 1 equal 2? Spot the error
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A defining features of learning mathematics is being able to read, write, and discover proofs. A proof is a method of communicating a mathematical truth to another person who speaks the "language" of mathematics. It's a way of showing whether a statement made is absolutely true or false. I recently came across a fallacious proof attempting to show that the integer one equals two – shown are the steps to accomplish this. Common sense dictates that this is impossible, but the proof is somewhat convincing to the untrained eye. However, most people with basic algebraic knowledge should be able to pick out the mistake, so take a minute or two to see if you can identify the incorrect step. If you're stuck, don't give up so quickly! It's easier th ...
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39542 |
bio_man |
2 years ago |
How smart are you? Try this test
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Here are some interesting puzzles for you to solve!What are the next two characters in the following sequences? - A B 1 C D 2 E ___ ___
- B F J N ___ ___
- O T T F F S S E ___ ___
- 3 3 5 4 4 3 5 5 ___ ___
You have 1 minute to complete each challenge. Once you're done, click the button to reveal the answers. Answers:- A B 1 C D 2 E F 3 – (two letters, one number in sequence)
- B F J N R V – (every 4th letter)
- O T T F F S S E N T – One Two Three Four Five Six Seven Eight Nine Ten
- 3 3 5 4 4 3 5 5 4 3 – (number of letters in each number spelled out in #3; e.g., “one” has 3 letters, “two” has three letters, etc.)
Now that you know the answers, how many ...
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1625 |
bio_man |
5 years ago |
Curry's paradox, explained
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At some point in your life, you've probably played this game of logic known as the missing square puzzle, or Curry's paradox - named after its inventor Paul Curry. This optical illusion is commonly used in mathematics classes to help students reason about geometrical figures, or rather to teach them to not reason using figures, but only using the textual description thereof and the axioms of geometry. It depicts two arrangements made of similar shapes in slightly different configurations. Each apparently forms a 13×5 right-angled triangle, but one has a 1×1 hole in it. As depicted in the animation, the illusion works because the diagonal of the two internal triangles is not a continuous slope from corner to corner. The overall connected shap ...
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16260 |
duddy |
8 years ago |
Which box has the car?
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Time for a riddle! There are 3 boxes. One of them has a car that you get to keep. On each box there is a statement. You know that only one of these statements is true.
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19592 |
duddy |
9 years ago |
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