I think if you look at this animation and think about it long enough, you’ll understand:
- Why circles and right-angle triangles and angles are all related
- Why sine is opposite over hypotenuse and so on
- Why cosine is simply sine but offset by π/2 radians
The sum of the exterior angles of any convex polygon will always add up to 360∘.
This can be viewed as a zooming out process, as illustrate by the animation below:
This animation shows that a circle’s perimeter equals to 2r∗π. As ShreevatsaR pointed out, this is obvious because π is by definition the ratio of a circle’s circumference to its diameter
In this image we can see how the ratio is calculated. The wheel’s diameter is 1. After the perimeter is rolled down we can see that its length equals to π amount of wheels.
Simple answer for “what is a radian”:
Logarithmic spiral and scale:
For example bezier curves visually:
He has also created MathBox.js which powers his amazing visualisations in the slides.
Here’s a GIF that I made that demonstrates Phi (golden number)
Math is always fun to learn. Here are some of the images that explain some things beautifully visually