right angle triangle calculator - problems

[oldbrewer]

this code finds 2 non hypotenuse sides that form a right angle triangle then checks if it is a multiple of a previous "find". it finds nothing after 65 72 97 ie it does not find 65 156 169.

J column is a list of prime numbers below 100

Sub Macro4()
'
' Macro4 Macro
' Macro recorded 13/08/2017 by bob
'


'
For j = 3 To 69
Cells(1, 8) = j
For k = j + 1 To 175
temp = j ^ 2 + k ^ 2: Cells(1, 4) = temp
temp1 = Sqr(temp): Cells(1, 5) = temp1
temp2 = Int(temp1): Cells(1, 6) = temp2
If temp2 = temp1 Then GoTo 100 Else GoTo 200
100 For z = 1 To 25
If Cells(z, 10) > k Then GoTo 150 Else GoTo 140
140 If j / Cells(z, 10) = Int(j / Cells(z, 10)) Then GoTo 142 Else GoTo 170
142 If k / Cells(z, 10) = Int(k / Cells(z, 10)) Then GoTo 144 Else GoTo 170
144 If temp / Cells(z, 10) = Int(temp / Cells(z, 10)) Then GoTo 200 Else GoTo 150
150 Sum = Sum + 1: Cells(Sum, 1) = j: Cells(Sum, 2) = k: GoTo 200
170 Next z
200 Next k
Next j
End Sub

 

[Eric W]

Just to put my 2 cents in . . .

There is a mathematical theory that says given any 2 integers i and j, where j > i, you can create a Pythagorean triple with these formulas:

a = j^2 - i^2
b = 2 * i * j
c = j^2 + i^2

That part is easy enough to prove algebraically. It's a little tougher to prove that you'll find every possible Pythagorean triple that way, but trust me, that's true too. Given that, it's easy to write a program to find them all:

Sub Triples()
Dim i As Long, j As Long, a As Long, b As Long, c As Long, Sum As Long

    Sum = 0
    For i = 1 To 100
        For j = i + 1 To 101
            a = j ^ 2 - i ^ 2
            b = 2 * i * j
            c = j ^ 2 + i ^ 2
            If WorksheetFunction.Gcd(a, b, c) = 1 Then
                Sum = Sum + 1
                Cells(Sum, "A") = a
                Cells(Sum, "B") = b
                Cells(Sum, "C") = c
            End If
        Next j
    Next i
            
End Sub

A few things of interest. A triple that is not a multiple of another triple is called a primitive.

Next, this algorithm sometimes creates numbers where a > b. If that's of concern, you can add a check for that and switch them. Finally, the triples aren't really in order. It would probably look better if they were sorted by column A, then column B.

Anyway, I put a lot of study into this kind of thing when I was younger, I hope there's something of interest in it!

 

[oldbrewer]

shg - yes it does - but it is bugging me why the original code never found ANYTHING beyond 65 72 97 - I will not give up and will insert artificial break points and print out intermediate values to solve it.....

 

[shg]

@Eric: Nice.

 

[oldbrewer]

Eric - thank you

I have found every unique right angle triangle up to sides of around 15000 and am running into precision problems - thinking about trying to make a long multiplication spreadsheet - I seem to think there is a long division way of getting square roots - do you know of it ?