a^2+b^2=2(c^2)

[spydragon]

this is not an assignment I was given but it is something I've been thinking about and I don't know how to solve it

I want a list of equations that use two variables that when I plug in any whole number value for the two variables they will give me solutions to the equation (a^2) + (b^2) = 2(c^2)

an example of what I want is the Pythagorean triples.

(a^2) + (b^2) = c^2

a = 2mn

b = (m^2) - (n^2)

c = (m^2) + (n^2)

can someone help me with this problem?

[spydragon]

all I want really is a nudge in the right direction

[John Cuthber]

More than a nudge but...

https://en.wikipedia.org/wiki/Formulas_for_generating_Pythagorean_triples

[spydragon]

should have clarified that, even though I am a fan of mathematics I have only learned pre algebra through part of geometry

(and I don't know if what I want exists), thank you anyway

Edited March 27, 2019 by spydragon

[HallsofIvy]

Sorry, I misread the question.

Edited April 8, 2019 by HallsofIvy

[uncool]

Spydragon: do you understand the reasoning behind the equations you gave for a^2 + b^2 = c^2?

[spydragon]

 

12 hours ago, uncool said:

Spydragon: do you understand the reasoning behind the equations you gave for a^2 + b^2 = c^2?

 uncool, yes but my reasoning goes only as far as a video I watched on how to do it. I used the same method but got an annoying square root of 2 to mess it up

[spydragon]

On 4/8/2019 at 8:56 AM, uncool said:

Spydragon: do you understand the reasoning behind the equations you gave for a^2 + b^2 = c^2?

@uncool yes but my reasoning goes as far as a video I watched on how to get it. I used the same method but got an annoying square root of 2 to mess it up.

[uncool]

What do you think is the reasoning behind those equations? In other words, I'm not talking about whether they work, but why they work - what train of thought led to their discovery. There is some interesting geometric reasoning that immediately gives the answer for a^2 + b^2 = 2c^2.

[Pasker]

OMG,i don't know the answer for it.