The hardest "What comes next?" (Euler's pentagonal formula)
Mathologer・2 minutes read
Mathologer created a new t-shirt design inspired by Jesko Mathis and Aaron Prince, exploring patterns in connecting dots on a circle to reveal formulas for partition numbers linked to prime numbers. Euler's pentagonal number theorem demonstrates how distinct partitions relate to even and odd numbers, with exceptions for pentagonal numbers, showcasing a visual pattern in partition calculations.
Insights
- The number of regions created by connecting dots around a circle follows a pattern, with the formula for the nth term being 2 to the power of n, as discussed by Jesko Mathis and Aaron Prince.
- Euler's pentagonal number theorem showcases exceptions to the rule of equal even and odd distinct partitions, particularly concerning pentagonal numbers, leading to a unique relationship between partition numbers and pentagonal figures.
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Recent questions
What is the significance of pentagonal numbers?
Pentagonal numbers relate to partition number calculations.
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Lec 5 | MIT 6.042J Mathematics for Computer Science, Fall 2010