Happy Friday almost July 2013!

This is a series of plots of the following:

1. x^2 + y^2 = n^2

2. x^2 + y^2 = n^3

3. x^3 + y^3 = n^2

4. x^3 + y^2 = n^2

5. x^3 + y^2 = n^3

For x, y, and n all integers. Plots are pointed for combinations where the result, n, is an integer. The range tested is 0 ≤ x ≤ 200 and 0 ≤ y ≤ 200. I used the TI nSpire CX CAS iOS app.

How many points?

1. x^2 + y^2 = n^2, 703 points

2. x^2 + y^2 = n^3, 55 points

3. x^3 + y^3 = n^2, 97 points

4. x^3 + y^2 = n^2, 375 points

5. x^3 + y^2 = n^3, 213 points, mostly when y=0

Program Outline: (for plot 1, similar format for the rest)

Define test()

Prgm

xs:={ }

ys:={ }

For k,0,200

For l,0,200

If iPart(√(k^2+l^2))=0 Then

xs:=augment(xs,{k})

ys:=augment(ys,{l})

EndIf

EndFor

EndFor

EndPrgm

And now to the fun part... Enjoy!

That's it for now - as always thanks for your support and words of encouragement and your questions. :)

Eddie

This blog is property of Edward Shore. 2013