# 3-D Torus/Trapezoid Formula

1. May 11, 2012

### Roger900

Hello,

Does the three dimensional curvature of a Torus prevent the use of the two dimensional mathematical trapezoid formulas (Pythagorean theorem) to solve for the length of a theoretical line that diagonally cuts a curved trapezoid?

For example, assume a Torus exists similar to the picture located in the attached file named " torus.gif "

As you can see in the picture, the Torus is comprised of trapezoids that are curving to form the structure of the Torus.

If you select a single trapezoid and draw a diagonal line, thus cutting the trapezoid, can you use the Pythagorean theorem to solve for the length of the diagonal line, or does the curvature of the trapezoid require the use of another mathematical formula?

For example, in the attached file named " Trapezoid.jpg ", a trapezoid is drawn with leg 'h' as the diagonal (or cutting leg) of the trapezoid. Can the length of leg 'h' be solved with the use of the Pythagorean theorem?

Thanks,
Roger

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