A Piece of the Pi: mathematics explained

A Piece of the Pi: mathematics explained is a Substack aimed at explaining complex mathematical concepts to intelligent general readers. It covers a wide range of mathematical topics such as number theory, geometry, probability, and algebra, translating intricate mathematical phenomena and theories into accessible insights.

Number Theory Geometry Algebra Probability Combinatorics Mathematical Puzzles Mathematical Physics Fractals and Patterns Game Theory Mathematical Biology

The hottest Substack posts of A Piece of the Pi: mathematics explained

And their main takeaways

Why your friends, on average, have more friends than you do

24 implied HN points • 04 Jul 15
  1. The friendship paradox explains why your friends have more friends than you on average.
  2. The phenomenon was first observed and is an interesting social phenomenon.
  3. Consider subscribing to access more content on this topic.

Primes in the Gaussian integers

6 implied HN points • 18 Aug 16
  1. The post discusses primes in the Gaussian integers.
  2. A Gaussian integer is a complex number of the form a + bi.
  3. The image in the post shows the prime numbers in the Gaussian integers.

Multiply-perfect numbers

6 implied HN points • 20 Sep 15
  1. A perfect number has divisors that sum up to 2 times the number itself.
  2. A number is multiply-perfect if divisors sum up to a multiple of the number.
  3. The post discusses multiply-perfect numbers and their properties.

The mathematics of Boggle logic puzzles

0 implied HN points • 20 Jun 15
  1. The article discusses the mathematics behind Boggle logic puzzles.
  2. The object of the game is to place fourteen letters into a grid.
  3. The post is for paid subscribers.

Self-similar polygonal tilings

0 implied HN points • 07 Jun 17
  1. The image shows a self-similar polygonal tiling by Michael Barnsley and Andrew Vince.
  2. Self-similar polygonal tilings are patterns that repeat themselves in a nested way.
  3. The concept of self-similar polygonal tilings is related to well-known examples like Penrose tilings.
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Penrose Land Cover by Daniel P. Huffman

0 implied HN points • 04 May 15
  1. The land cover map of the continental US was created using Penrose tiles by Daniel P. Huffman.
  2. The traditional method for creating such a map differs from the Penrose tile approach.
  3. The post is for paid subscribers only, with options to subscribe or sign in if already a paid subscriber.

Knot mosaics

0 implied HN points • 23 Sep 16
  1. This post discusses knot mosaics created by Samuel J. Lomonaco Jr and Louis H. Kauffman.
  2. A knot mosaic is made by tiling a rectangular grid with 11 types of symbols.
  3. The post is for paid subscribers only.

When does a random jigsaw puzzle have a unique solution?

0 implied HN points • 19 May 16
  1. The post discusses when a random jigsaw puzzle has a unique solution.
  2. It focuses on the puzzle size and the number of different edge types.
  3. Consider how the size of the puzzle influences the required number of edge types.

Christopher Wren and John Wallis

0 implied HN points • 04 Jun 15
  1. The post is about Christopher Wren and John Wallis.
  2. The author visited Emmanuel College and took a picture of the chapel.
  3. The post is for paid subscribers only.

Links of links, and higher structures

0 implied HN points • 07 Sep 15
  1. The post discusses the concept of Brunnian links, which are loops connected in a way that of one loop is cut, all others become free.
  2. The post is for paid subscribers only, promoting a deeper dive into the topic.
  3. There are options to subscribe or sign in for those interested in accessing the content.

Fractals, Fibonacci, and factorizations

0 implied HN points • 30 Aug 15
  1. The Fibonacci sequence is generated by adding the previous two numbers.
  2. Fractals, Fibonacci, and factorizations are discussed in the post.
  3. The content of the post may only be accessible to paid subscribers.

Keleti's Perimeter to Area Conjecture

0 implied HN points • 16 Aug 15
  1. Keleti's Perimeter to Area Conjecture focuses on the ratio of perimeter to area in squares.
  2. By dividing the perimeter of a square of side 1 by its area, a ratio of 4 is obtained.
  3. The post discusses the concept further with adjacent unit squares sharing an edge.

Average pace and the Universal Chord Theorem

0 implied HN points • 11 Jul 15
  1. The post discusses the concept of average pace in relation to running races.
  2. It mentions the Universal Chord Theorem.
  3. The example provided is for a three-mile race with a six-minute per mile pace.

The complexity of integers

0 implied HN points • 13 Dec 15
  1. The complexity of an integer is defined by the minimum number of 1s needed to build it using parentheses, addition, and multiplication.
  2. This post discusses the concept of integer complexity and how it is calculated.
  3. The post is available for paid subscribers only.

The Gamma Function and Fractal Factorials!

0 implied HN points • 24 May 15
  1. Fractal image created using iterations of the Gamma function.
  2. Gamma function is a continuous version of the factorial function.
  3. Post is for paid subscribers only.

A hidden signal in the Ulam sequence

0 implied HN points • 30 Jul 15
  1. The Ulam sequence is a sequence of positive integers.
  2. Each term in the sequence is the smallest integer expressible in a unique way.
  3. A hidden signal is observed in the Ulam sequence.

Road interchanges with minimal numbers of bridges

0 implied HN points • 18 Aug 18
  1. The smallest number of bridges necessary to build a complete _n_ way road interchange without changing lanes is _(n-1)(n-2)/4_ for even values of _n_.
  2. The information was presented in a paper by Valentas Kurauskas.
  3. The paper can be found at _arxiv.org/abs/1612.07888_.

The onion decomposition of a network

0 implied HN points • 25 Jan 16
  1. The onion decomposition is a network fingerprinting technique.
  2. It helps identify structural properties of a network.
  3. The technique is valuable for analyzing network structures.

The sandpile model with a billion grains of sand

0 implied HN points • 04 Nov 15
  1. The sandpile model involves a billion grains of sand.
  2. There is a picture illustrating a stable configuration in the abelian sandpile model on a square lattice.
  3. The post is available for paid subscribers only.

A Curious Property of 82000

0 implied HN points • 17 May 15
  1. The number 82000 has interesting properties in different number bases.
  2. In base 2, 82000 is 10100000001010000.
  3. This post is for paid subscribers only.