It has been a very difficult time of late. The sudden unexpected passing of the person who has had the most significant developmental influence on my life continues to cast a long shadow over my life (as it should). My thoughts and focus has been poor. I still learn a lot and derive a lot of satisfaction from Mathematica Stackexchange.
This post is to share a beautiful answer by user ybeltukov that converts the problem to a simpler spherical one and exploits the symmetry. The answer is here (beautiful).
This is a readable book. I enjoyed it. It makes a valliant attempt to explain quantum theory. The click analogy is useful. However, I was less convinced by the style and approach than I thought I would. The authors are clear and deliberate and try to focus on concepts and use the minimum amount of Mathematics required to get their aim across.
I have consistently enjoyed Philip Ball’s books. I particularly enjoy his rich writing style. I did find this book, however, difficult to engage with. The book does provide a comprehensive and detailed exploration of the mergence of scientific thinking and empirical science from the medieval period. It is largely focussed (therefore) on the 16 th and 17 th century. The cultural, religiious and individual personalities interacting to reveal a more interesting and complex emergence of science from “Natural Magick” and curiosity (the theme of the book) is interesting and edifying.
The book’s length and detail did exceed my concentration. Perhaps, this reflects more about me and my time constraints, but it was less enjoyable than Ball’ other wonderful works.
I am enjoying Steven Strogatz second edition of “Non-linear Dynamics and Chaos”.
This post is motivated by this. The following gif relates to the model for insect outbreak. It shows the critical point parameter surface.
The differential equation: . Note the fixed point is unstable.
This is a very enjoyable read. The author has a very entertaining and engaging writing style. The book starts looks at psychological aspects of human relationship to numbers. Thereafter, we are taken on a journey through triangles, circles, conic sections, complex numbers, calculus, cellular automata and proof and more. Pi, e, and i are characters and the amazing appearance and connectedness is expressed. This is a very rich journey through history and exposition of the variety of applications some seemingly esoteric areas have found. I particularly enjoyed the sections on roulettes.
The book is not a technical explanation but invites the reader to play: whether it is origami to produce a parabola, rolling one coin over another, or looking for patterns in your cup to tea. However, the concepts are expressed clearly and convincingly.
The complex dynamic interaction between development of mathematics and its applications: motivations, personalities and serendipity in complex feedback loops , shows what a wonderfully human endeavour Mathematics is.
This post is motivated by Bellos’ “Grapes of Math”:
Hyperboloid from straightlines
I could not resist the “cardioid” roulette:
and just for fun rolling coins:
This is an excellent informal introduction. It is written clearly, uses simple but illustrative worked examples with helpful graphics. It covers the title topics and uses electrostatics as a tangible application for illustration. There a lot of problems and solutions at the end.