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## Main Question or Discussion Point

Let's assume I simulate a number of particles using a computer program. I teach the particles to move according to F=ma. The F acting on each particle will be the sum of all forces to other particles according to F=m1*m2/distance^2.

I give the particles a set of initial positions and velocities and I automatically get conservation of linear momentum, conservation of angular momentum, and conservation of energy, just like that. I haven't actually programmed those properties into code.

Basically I've only used F=m*a, v=a*t, p=v*t, action=reaction, the pythagorean theorem and some sums. Does it come from F=m*a, from action=reaction, is it a property of isometric space, or all of them?

I give the particles a set of initial positions and velocities and I automatically get conservation of linear momentum, conservation of angular momentum, and conservation of energy, just like that. I haven't actually programmed those properties into code.

**Where does the conservation come from?**Basically I've only used F=m*a, v=a*t, p=v*t, action=reaction, the pythagorean theorem and some sums. Does it come from F=m*a, from action=reaction, is it a property of isometric space, or all of them?