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Odd Squares as Difference of Triangular Numbers (visual proof)
Alternating Sum of Triangular Numbers (visual proof without words)
Products of Odd Squares and Triangular Numbers (visual proof - updated version)
A Triangular Number Identity I (visual proof)
A Multiplicative Triangular Number Recurrence (visual proof)
Proof Without Words: Sum of Triangular Numbers
Triangular Numbers Explained
Squares Modulo 3 (visual proof)
Triangular Numbers | 1+2+3+...+n = n(n+1)/2
Calculating triangular numbers the fast way: visual proof
Perfect Numbers (even ones) are Triangular (visual proof) -- with bonus open problem!
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Last Updated: August 13, 2026
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