16 GIFs That Will Actually Help You In Maths Class

The one time it's actually productive to be reading BuzzFeed in school.

1. Here's proof that Pythagoras' theorem really works.

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Pythagoras' theorem says that the square of the hypotenuse (the side of the triangle opposite the right angle) is equal to the sum of the squares of the other two sides.

And look! Here you can see that squares of the two shorter sides are equal in area to a square of the longest side.

2. And here's a slightly longer explanation of why a² + b² = c².

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The hypotenuse – the longest side of the triangle – is c, and the other two sides are a and b. Watch the GIF to the end and you'll be a Pythagorean genius.

3. This is how pi works.

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The circumference of a circle is pi multiplied by the diameter So if you roll out the circumference into a straight line, it'll be pi diameters long. Voila!

4. This is why the area of a circle is πr².

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You know the circumference is 2πr (where r is the radius). If you cut up the circle and roll it out to a triangle, the base of that triangle has length 2πr and its height is r.

The area of a triangle is ½ x base x height, resulting in πr².

5. This is how a straight line can draw out a curved shape.

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This straight line, angled at about 45º, is tracing out a hyperboloid. A hyperboloid is a curved hourglass shape that can be made just with straight lines.

6. Here are two more examples of straight lines tracing hyperboloids.

The one on the right shows the full hyperboloid.

7. Here's what tan(x) actually has to do with tangents.

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A tangent is a line that touches a surface but doesn't cross it, like the horizontal line across the top of the circle in this GIF.

You can see the line coming from the centre of this circle crossing the tangent line and creating the tangent function lines you can see.

8. Here's another way of looking at it.

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Notice how the tan(x) line goes through the x axis at multiples of pi.

9. This is how to construct a square using circles.

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Time to get that compass out.

10. This is how to draw an ellipse with a piece of string.

11. This shows the relationship between sin(x) and cos(x).

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See how they're displaced by 90º.

12. This is how radians work.

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If you make an arc with the length of one radius of the circle, it will have an angle of one radian.

13. This shows why angles in the same segment of a circle are equal.

14. This is how to make a fractal.

Dino / CC / commons.wikimedia.org

This is a type of fractal called a Sierpinski Triangle. It's made by splitting one triangle up into four triangles, removing the middle one, and then repeating that basically forever.

15. And this is how a fractal just keeps going forever.

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And ever and ever...

16. And finally, how to draw a sumo wrestler using circles.

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A very important mathematical concept.