Geometry and Numbers – negative ones – “a minus times a minus is a plus”

To accommodate positive and negative numbers we need two extended number lines, with their zeros at the same place

Then multiplication of two negative numbers will always give a positive result, following the same geometrical structure.

The start, where the multiplier begins at 1

mult pic negative 0

Now the 1 connects with the multiplicand -3

mult pic negative 1

The multiplier is now placed at -2

mult pic negative 2 6

And the parallel line from -2 connects to the 6 on the target line

mult pic negative 3

This is so geometrical, and there is no “funny business”. None of the “ought to be 6”. No stuff about the distributive law.

The only geometry needs the Pythagoras theorem, and this will be the next post.

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Filed under arithmetic, education, geometry, geostruct, negative numbers, Number systems, Uncategorized

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