Pappus Chain

​ ​ Ruisi Ma & Yimeng Liu Background Properties

Arbelos Center of the Circle Art： The term "arbelos" means All the centers of the shoemaker's knife in Greek. An arbelos is combined circles in the Pappus chain The World Necklace Mathematically inspired Poster with three semicircles which are shared with one of are located on a common , for the following ​ ​ (2015) the others, all on the same side of a straight line that reason. The sum of the distances from the nth circle contains their diameters. These three circles are also to the two centers U (Largest)and V (Second) of tangential from each other. (Weisstein, 2020) the arbelos circles equals a constant: (Weisstein, Cosmic Evolution: The Rise of Complexity in Nature by Eric J Original: Chaisson . The Arbelo was first introduced in the book of 2020) Lemmas.The book of Lemmas is Thābitibn Qurra's @koji_glass (2019) Coordinate ​ book attributed to Archimedes. It consists of fifteen If r = AC / AB then the center of the nth circle is: propositions on circles. From Wikipedia. Further Research:

Pappus Chain 1. How kind of applications are there for the

Starting with the circle P 1 pappus chain? tangent to the three (Weisstein, 2020) 2. How could the properties of the pappus semicircles forming the Distance from bottom to nth circle’s center is n chain also apply to the steiner chain? ​ 3. How to use the pappus chain to calculate the arbelos, construct a chain of P i , all time radiums: ​ ​ ​ area in geometry? tangent to one of the second small interior circles Using inverse geometry theory, and to the largest exterior one. Constructing an The circle with diameter AB Reference: infinite chain of tangent circles is called the Pappus gets mapped to the vertical line koji_glass. (2019). Picuki. Www.Picuki.Com. ​ ​ chain (left figure).(Weisstein, 2020) through B′ , and the circle with https://www.picuki.com/media/1786800340121983561 Lambie-Hanson, C. (2017, November 30). Circle Inversion and the diameter AC gets mapped to the Pappus Chain. Point at Infinity. Mathematician: https://pointatinfinityblog.wordpress.com/2017/11/30/circle-i Pappus was an ancient Greek mathematician. He vertical line through C′ . Our nversion-and-the-pappus-chain/#post-5609 SolunaDesign. (2015). Items similar to The World Necklace(Pappus was also the last great geologist at Alexander Pappus chain is transformed by inversion into an Chain) Mathmatically Inspired Poster on Etsy. College. His book. "Anthology of Mathematics" is infinite tower of circles. From that we could find the Etsy.https://www.etsy.com/listing/237094720/the-world-necl of great significance to the history of mathematics. ace-pappus-chain height of the circle : H3 = 3d3 = 6r Weisstein, E. W. (2020, April 25). Arbelos. Mathworld.Wolfram.Com. (Lambie-Hanson, 2017) https://mathworld.wolfram.com/Arbelos.html