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A GEOMETRIC INTERPRETATION OF EQUAL SUMS OF CUBES
Abstract:
The geometric interpretation of the Pythagorean Theorem is that the square of diagonal of a rectangle is equal to the sum of squares of two sides. We will discuss some other geometric interpretation of the equivalent forms of equations. The purpose of the work is to find a geometric interpretation of equal sums of cubes in the form
.
Problem: find a geometric interpretation of equal sums of cubes in the form .
Solution:
We know the Pythagorean Theorem:


Let us take a cuboid.

From the triangle ABC:

From the triangle ACD:


Let us cut an angle from this cuboid. We get the corner:

We have .
Let’s put our corner in the zero vector point:

Then A=(0,0,0), D=(a,0,0), C=(0,b,0), B=(0,0,c).

Similarly,







The magnitude of cross product of two vector gives us the area of the parallelogram. So, the area of the triangle BCD is one half from the magnitude of cross product......

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Approximate Word Count: 450
Approximate Pages: 2 (250 words per double-spaced page)

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