Pythagoras Number Sets
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Normal (2D) Pythagoras Theorem Numbers
Pythagoras theorem applies to a triangle with lengths a, b and c as shown in diagram.
It indicates that the square of the hypotenuse is equal to the sum of the squares of the other two sides
If you look at the diagram, this means that a2 + b2 = c2
right angle triangle with sides labelled a, b and c
The table below indicates some of the "integer" values that obey the rule and form right-angled triangles.
345 and all multiples e.g.6810
51213 and all multiples e.g.102426
72425 and all multiples e.g.144850
81517 and all multiples e.g.163034
94041 and all multiples e.g.188082
123537 and all multiples e.g.247074
202129 and all multiples e.g.404258
Extended (3D) Pythagoras Theorem Numbers
Pythagoras theorem can be extended for trianglular prisms with lengths a, b c, and diagonal d as shown in diagram.
It indicates that the square of the diagonal is equal to the sum of the squares of the three main edges
If you look at the diagram a2 + b2 + c2 = d2
right angle prism with edges labelled a, b and c
The table below indicates some of the "integer" values that obey the rule and form right-angled prisms.
1223
1489
2446
2367
26911
3669
4479
48812
5101015
66811
Sum of 3 Cubes
There are very complex mathematical theories as to whether any set of integers exist which could fulfil the equation ...... a3 + b3 = c3
However, integer solutions for extended version of the cubic equation ...... a3 + b3 + c3= d3 ...... include
1689
2121618
3456
3101819
4356
5346
6189
681012
7141720
8169
861012
9121518
1031819
108612
1221618
1215918
12162024
1471720
1591218
1621218
16122024
1771420
1831019
20121624
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