Math equations are not magic! - You can see for yourself

Posts on the "Why math?" series

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What I mean by this can be shown



Look at the green square.
When it's cut in half by that red line, it makes two right-angled triangles.

Let's label the lines of the triangle A, B and C
Where C is the hypotenuse. 

Remember the "Pythagorean theorem"?





First, you have to understand what A2 even means. Why is it to the power of 2?
Because it's A*A - It appears twice.

Why do we then say A2 is "A squared"? Because A by A makes a 2-dimensional shape that is A long and A wide, a square. 

So, now that you understand this, let's visualize the Pythagorean theorem again:


That is all that the formula is saying. 
Now go back to the 2nd picture in this post and how many green triangles fit inside of the red square.
You should conclude that exactly four green triangles make up the bigger red square.
Since the green triangles are exactly half of the green square, then we can conclude that:
Two green squares fit inside the red square.
That is,   a2 + b2 = c2

That's all that's going on! We can talk about how the red square is twice as big or just write that simple formula. It's no "mysterious property" or "law" or "rule", it just is.





For the more mathematically advanced of you, take a look at this mathematical formula and explanation for the relationship between the size of an object, light source and shadow size:



With this, I got a last formula that can tell you exactly where a light source is just by finding out how big of a shadow an object of known size produces and it's distance from the shadow. It's no magic, only logic and geometry.

The same applies to the inverse square law of (eg) gravity:


The "law" for the strength of gravity is literally, again, just logical geometry!

I can go on and on with this.