Co-prime Art

Transcript

Co-prime ArtThe "Co-prime art" section demonstrates a mathematical relationship by creating patterns with thread on a circle of pegs. The pattern created depends on two numbers: The total number of pegs on the circle. The thread-gap, which is the number of pegs you count to get to the next point. We start with 1 and have to reach the last number The central observation is that in some diagrams, the thread touches every single peg, while in others, it does not. The explanation for this difference is related to whether the two numbers (pegs and gap) are co-prime. Here is a breakdown of the examples shown: When the numbers are NOT co-prime: The thread does not touch every peg. It creates smaller, separate patterns. Discussing these diagrams First diagram 12 pegs and thread gap 4 The numbers 12 and 4 are not co-prime. As a result, the thread only touches 3 of the 12 pegs, creating a simple triangle. Third diagram 16 pegs and thread gap 6 The numbers 16 and 6 are not co-prime. As a result, the thread only touches even numbers of the 16 pegs, creating a star. Fourth diagram 24 pegs and thread gap 6 The numbers 24 and 6 are not co-prime. As a result, the thread only touches 4 of the 24 pegs, creating a square When the numbers ARE co-prime: The thread touches every peg on the circle before returning to the starting point, creating a single, intricate star-like pattern. Second Diagram: 13 pegs and the thread-gap is 3. The numbers 13 and 3 are co-prime. As a result, the thread visits every one of the 13 pegs, creating a complete star shape. In summary, the rule is: The thread art will touch every peg on the circle only when the number of pegs and the thread-gap are co-prime numbers.