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The law of oriented sines

In geometric algebra a triangle is characterized by the three side vectors:

a+b=c.

Taking the outer product of this formula with a, b and c gives:

a^c = a^b = c^b.

These three parallelogram shaped bivectors are illustrated below. All three overlap in the white triangle area. The three bivector areas and orientations agree.

You can drag the three triangle points around.

[ GA with Cinderella ]

Soli Deo Gloria. Created with Cinderella
by Eckhard Hitzer (Fukui).