Category: Math

  • The Parallel Postulate

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    Take a piece of paper and draw a dot anywhere on the page. Let’s call that dot P. Now, grab a ruler and draw a straight line anywhere else on that page (just make sure it doesn’t go through point P.) Call that line L. Euclid’s parallel postulate states that there is only one line—just…

  • Calculating the Circumference of the Earth

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    How it was calculated by Eratosthenes over 2000 years ago. During the 3rd century BC, a man named Eratosthenes ventured to calculate the circumference of the earth (yes, people did know the Earth was round even back then). Of course, advanced technology wasn’t available at that time to do most of the work for him.…

  • Euler’s Number

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    2.718281828459045235360287… I’ve come across the value ‘e’ many times before; it’s one of those particular numbers that we hear mathematicians speak about quite frequently, especially in the case of Euler’s Identity, which is nicknamed the most beautiful formula in mathematics. But I realised that I know very little about what the number really represents. So…

  • Proof 2 of Pythagoras’ Theorem

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    Here’s a second proof of the legendary Pythagoras’ Theorem: In this diagram: It follows that the area of the large square = C^2. C^2 = 4 (1/2 x A x B) + (B – A)^2 This is the area of the small square added to the areas of the four right-angled triangles. When simplified: C^2…

  • Proof 1 of Pythagoras’ Theorem

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    We’ve all come across the legendary Pythagoras’ Theorem in Highschool geometry: a theorem which states that in a right angled triangle, the length of the hypotenuse (squared) is equal to the length of the opposite (squared) plus the adjacent (squared), or in more familiar terms: c2 = a2 + b2 There are over 600 ways to prove…

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