Citations:inverse Pythagorean theorem

English citations of inverse Pythagorean theorem

• 2009, J.M. Aarts, Plane and Solid Geometry, →ISBN, page x:

  Another basic assumption concerns the existence of perpendicular lines; whether two given lines are perpendicular is decided with the help of the inverse Pythagorean theorem.

• 2012, Nicholas Gauguin Houghton-Larsen, “On the Extension of Complex Numbers”, in Rose-Human Undergraduate Mathematics Journal‎^[1], volume 13, number 2:

  Finally, let the GSA be normed and equipped with at least three imaginary units; choosing $\xi :=\alpha +\beta \kappa _{1}\in {\mathcal {S}}$ we then have $|\xi \circ \kappa _{2}+\xi \circ \kappa _{3}|=|\xi \circ (\kappa _{2}+\kappa _{3})|={\sqrt {\alpha ^{2}+\beta ^{2}}}{\sqrt {2}}$, whereas $|\xi \circ \kappa _{2}|=|\xi \circ \kappa _{3}|={\sqrt {\alpha ^{2}+\beta ^{2}}}$ and thus $(\xi \circ \kappa _{2})^{\text{ˇ}}\cdot (\xi \circ \kappa _{3})^{\text{ˇ}}=0$ (inverse Pythagorean Theorem).