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→Corollary: No set of three lines with prime numbers as lengths can form a right triangle: focused use of named terms toward congruous understanding of equivalent concepts in math. An evergreen liberal arts venture
<center>[[image:Pythagoras.gif]]</center>
<center>[[image:Pythagoras.gif]]</center>
==Corollary: No set of three lines with prime numbers as lengths can form a right triangle==
==Corollary: No three lines with prime numbers as lengths can form a right triangle==
Indirect proof: Let's describe a situation where lines with the lengths of three prime numbers ''do'' form a right triangle and see what follows.
Indirect proof: Let's describe a situation where lines with the lengths of three prime numbers ''do'' form a right triangle and see what follows.
:Corollary to assumption: Through the definition of prime numbers such as described in the first "conceptualization" section, if any pair of positive integers ''n'' and ''o'' have an common integral factor ''f'' apart from one and themselves, they are not prime because they ''both'' have a non-prime type of positive integral factor; in fact it's the same one.
:Corollary to assumption: Through the definition of prime numbers such as described in the first "conceptualization" section, if any pair of positive integers ''n'' and ''o'' have an common integral factor ''f'' apart from one and themselves, they are not prime because they ''both'' have a non-prime type of positive integral factor; in fact it's the same one.
Conditional sub-proof to be proved: ''Assuming no pair of prime numbers matches the set having the conditions described, no set of three lines with prime numbers as lengths can form a right triangle.''
Conditional sub-proof to be proven: ''Assuming no pair of prime numbers can possess the qualities of the pair set with the described factor, no three lines having prime numbers as lengths can form a right triangle.''
That is, it is to be proved that the first proposition (the condition) leads to the second.
That is, it is to be proven that the first proposition (the assumption for a conditional proof) leads to the second.
[[Category:Plane Geometry]]
[[Category:Plane Geometry]]
[[Category:Mathematics]]
[[Category:Mathematics]]
[[Category:Geometric Theorems]]
[[Category:Geometric Theorems]]