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Formulas for figurate numbers

I look at sequences of triangular numbers, square numbers, and oblong numbers. Using pictures, I derive several formulas for these sequences. Some formulas are recursive and some are explicit. #NotThatKindOfExplicit

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Pentagonal Tetrahedral and Triangular Number Pattern Rule
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Pentagonal Tetrahedral and Triangular Number Pattern Rule

Olympiad level counting  (Generating functions)
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Olympiad level counting (Generating functions)

From Child Prodigy to Winning Fields Medal, Nobel of Math
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From Child Prodigy to Winning Fields Medal, Nobel of Math

The Professor Who Taught People How To Think (1962)
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The Professor Who Taught People How To Think (1962)

The Oldest Unsolved Problem in Math
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The Oldest Unsolved Problem in Math

The Most Controversial Idea In Math
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The Most Controversial Idea In Math

Egyptian fractions: Jones Math Ed Problem Solving with Dr. Jones & Lucy
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Egyptian fractions: Jones Math Ed Problem Solving with Dr. Jones & Lucy

John Cleese’s Brillian Take on Religion & 'Life of Brian' | The Dick Cavett Show
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John Cleese’s Brillian Take on Religion & 'Life of Brian' | The Dick Cavett Show

1986: How to Spot the Upper Class | That's Life! | BBC Archive
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1986: How to Spot the Upper Class | That's Life! | BBC Archive

One reporter finally had enough
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One reporter finally had enough

Pascal's Triangle and Combinations
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Pascal's Triangle and Combinations

Complex number fundamentals | Ep. 3 Lockdown live math
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Complex number fundamentals | Ep. 3 Lockdown live math

Math Antics - Number Patterns
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Math Antics - Number Patterns

Polyhedral Numbers and k-Polytopes
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Polyhedral Numbers and k-Polytopes

The Bob Newhart Toupee Sketch That Broke Dean Martin
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The Bob Newhart Toupee Sketch That Broke Dean Martin

AfterMath: Polygonal Numbers
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AfterMath: Polygonal Numbers

Sum of Triangular Numbers I (visual proof)
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Sum of Triangular Numbers I (visual proof)

A Sudoku Secret to Blow Your Mind - Numberphile
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A Sudoku Secret to Blow Your Mind - Numberphile

The French Do Not Care About Work
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The French Do Not Care About Work

We're 99.9% sure this pattern is true, but no one can prove it
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We're 99.9% sure this pattern is true, but no one can prove it

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