# 92.48 The upside-down Pythagorean theorem

@article{Richinick20089248TU,
title={92.48 The upside-down Pythagorean theorem},
author={Jennifer Richinick},
journal={The Mathematical Gazette},
year={2008},
volume={92},
pages={313 - 316}
}
Introduction A triple of positive integers (a, b, c) is a Pythagorean triple if, and only if, a + b = c. Positive integers a and b will also be the lengths of the sides of a right-angled triangle and integer c will be the length of the hypotenuse. Let d equal the length of the segment that is perpendicular to the hypotenuse and that passes through the vertex of the right angle. It can then be proved that a~ + b' = d . We shall call the triple (a, b, d) an upside-down Pythagorean triple. The… Expand
3 Citations
Theorems on Pythagorean Triples and Prime Numbers
Relationships among natural numbers constituting a Pythagorean triple (PT) and between these natural numbers constituting the Pythagorean triples (PTs) and Prime Numbers (PNs) have been found. TheseExpand
Weighted Harmonic Means
The purpose of this study is to develop a conception of the differential subordination involving harmonic means of the expressions $$\psi (p(z), zp'(z);z)$$ψ(p(z),zp′(z);z), where p is an analyticExpand
Fermat’s Zero Theorem
Fermat’s zero theorem is stated as follows: It is impossible to separate a square of a difference of two natural numbers into two squares of differences, or a cube power of a difference into two cubeExpand

#### References

SHOWING 1-2 OF 2 REFERENCES
Euclid's Elements of Geometry
• Nature
• 1901
IF Euclid is to continue as the foundation of geometrical teaching in our schools, this work must b very warmly welcomed. The exact order of Euclid is followed, but (as the editors inform us) with noExpand
Mathematics without (many) words -upside down Pythagorean theorem
• The College Mathematics Journal
• 2001