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GalFisk t1_jedz4kt wrote

Draw him a number line, with 0 in the middle. Show how adding two numbers moves you right, then right again. Show how subtracting two numbers moves you right, then left. Show how adding a negative number moves you left. Then tell him that subtracting a negative number means turning that last operation around once more, meaning you go to the right again. Every minus is a turn.

Edit: if you really want to fry his brain (alternatively inspire him to become a mathematician), tell him that there's also a way to turn away from the number line, and go above or below it.

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gg_wellplait t1_jee36vm wrote

Please fry my brain...how do you turn away from the line???!

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GalFisk t1_jee40gx wrote

With imaginary numbers. They go up and down instead of left and right. If you combine them with real numbers, you get to do math in two dimensions.

I don't know a lot about what it's good for, but I know it has its uses.

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Isolus_ t1_jee7el1 wrote

You could even go two dimensions further and use quaternions...

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GalFisk t1_jee7h79 wrote

Cool, what are those good for?

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Isolus_ t1_jee8pvb wrote

They are often used to describe rotations in the 3D world. So when you have a camera drone (multicopter) there is a good change that they are used to process the sensor inputs (gyroscope/accelerometer) and calculate the corrections needed for a stable flight.

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GalFisk t1_jee92xq wrote

I saw a video on that. They had arrows pointing right, up and front, and connected them end to end in order to make a new arrow that pointed to the destination. Are quaternions the same as making calculations using x, y and z coordinates?

They also used trigonometry to transform back and forth between coordinates and angles.

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Isolus_ t1_jeeeqwy wrote

There are different ways to achieve this and it's hard to say what you have seen. The "classical" and "easy" approach is to use vectors and apply rotation matrices. But for a flying device you often rotate around an arbitrary axis and not around x, y or z. That is where quarternions come in handy. They can represent a rotation around an arbitrary vector. But they are harder to understand so most teaching of those concepts is done the "classical" way. Quaternions are also numerically stable. Computers can only represent an approximation of a number (for example you can't store Pi, only the beginning). Using matrices it's happens more easily that an error introduced through these approximations changes your result a lot.

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EveningSea7378 t1_jee3178 wrote

> tell him that there's also a way to turn away from the number line, and go above or below it.

Only if you totaly change the deffinition of what your numberline is on the way. You can not find i in the natural numbers.

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mikeholczer t1_jee64gg wrote

The same can be said about negative numbers or real numbers.

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