« on: Yesterday at 21:29:32 »
Quote from: petelamana
geometric solution to the division of two integers, a/b.By "Geometric", doe you mean the whole "Ancient Greek Mathematician" version of geometry, which only accepts solutions that can be done in a finite number of steps, with just a compass and straight-edge?
If so, I think I have one solution:
- Create a number line, marked in integers
- At right angles to this, create another number line, marked in integers, and passing through 0* (ie now a number plane)
- Mark a on one axis, and b on the other
- Draw a line between a and b. This represents the ratio a/b.
Now, how useful it is depends on what you want to do with this ratio.
A typical application might be to divide a third number "c" in the ratio a/b:
- Mark c on one axis
- Draw a line through c, parallel to the a-b line
- Where this new line crosses the other axis is the result of c divided in the ratio of a/b
Maybe you can be more specific about what applications you have in mind for the ratio of a/b?
*Ancient Greek Mathematicians didn't really believe in zero. But this construction only uses a compass and straightedge...
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