Precious Ratios

By G. Adam Stanislav

For thousands of years mathematicians and artists studied the golden ratio. Later they developed the silver ratio. This book develops the general formula for creating any number of precious ratios, compatible with the ideas behind the golden and silver ratios. As an example, it shows how to create and compute the values of the iridium ratio and the platinum ratio. It includes C++ classes to compute the value of any precious ratio, and a sample C++ code showing how to use the classes.

• Language: English
• Publisher: Time Travel Press
• Release date: Oct 5, 2014
• ISBN: 9780971646100

G. Adam Stanislav

Born 23 April 1950 in Bratislava, Stanislav was graduated in 1968 from Gymnázium Jura Hronca in Bratislava, with specialization in mathematics and computer programming. He holds graduate degrees in psychology from Komenský University in Bratislava and in canon law from Gregorian University in Rome. His writing, both fiction and non-fiction, was published in Slovakia, Czech Republic, Italy, Vatican and the United States. He has lived in Bratislava, Český Krumlov, Vienna, Rome, Washington and Pittsburgh. He is currently retired in Wisconsin. He was active in the anti-Communist underground in Czechoslovakia until he escaped to Austria in 1979. He became a US citizen in 1990 on the same day his home country rebelled against Communism in the Velvet Revolution. He enjoys visiting his beloved Bratislava as often as his financial situation and his failing health permit.

Book preview

Precious Ratios

The Fun with Numbers Series

by G. Adam Stanislav

Time Travel Press

Precious Ratios

A book in the Fun with Numbers series.

Copyright © 2014 G. Adam Stanislav.

All rights reserved. No part of this book may be reproduced or transmitted in any form by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the author.

Published by Time Travel Press logo Time Travel Press.

Smashwords edition ISBN: 978-0-9716461-0-0.

Mathematical notation typeset in LaTeX .

This ebook is licensed for your personal enjoyment only. This ebook may not be re-sold or given away to other people. If you would like to share this book with another person, please purchase an additional copy for each reader. If you’re reading this book and did not purchase it, or it was not purchased for your use only, then please return to your favorite retailer and purchase your own copy. Thank you for respecting the hard work of this author.

In loving memory of Professor Viera Šimčisková,

the best mathematics teacher the world has seen.

Precious Ratios TOC

Table of Contents

Introduction

1—Golden Ratio

2—Silver Ratio

3—Exploring the Precious Ratios

4—Splitting the Line

5—The Cheat Sheets

6—Iridium Ratio

7—Platinum Ratio

The Appendices

About the Author

For a more detailed TOC, please use your ebook reader’s navigational system.

Precious Ratios

Introduction

Recently, I was working on a project, for which I needed to calculate the value of a constant I named the platinum ratio. It was a variation of the well-known golden ratio and another, known as the silver ratio.

While calculating the value of the platinum ratio, which, by the way, is described in Chapter 7 of this book, I had to figure out all kinds of formulae. I coined the result of this work the precious ratios. And since I went through all that effort, I thought perhaps someone else might find it useful for their own work. To save them from having to re-discover what I have discovered already, I decided to write this book.

Even if you do not need to calculate a new precious ratio, I hope you will at least find this book interesting.

G. Adam Stanislav

If you are not familiar with mathematical notation, worry not, it is all explained as needed. Though you can also find the wikipedia article titled "List of mathematical symbols" useful reference.

Also, www.numericana.com/answer/symbol.htm offers interesting insights into the history of that—and other—symbology.

If, however, you are wondering, why we are using mathematical notation, if we need to explain it in plain English anyway, the more important question is, why do we have to explain it in the first place? Does anyone with at least a high-school education need to be told what H2O is? Of course not. They were taught the international language of chemistry at school. So, what kind of school teaches mathematics without teaching mathematical notation? Certainly, the high school I went to taught us the notation. If yours did not, you were cheated!

The mathematical notation is no different from chemical formulae, sheet music, street signs and many other international symbols. Only about 2% of the world’s population understands English. And not even all of the 2% are fluent in it. But among the remaining 98%, anyone with an interest in numbers can presumably read the mathematical notation, and so they can understand what this book is saying even if they cannot understand a single word that explains it.

That is why we are using mathematical notation.

Precious Ratios 1

For thousands of years mathematicians have been fascinated by certain ratios of two numbers a and b whose ratio seemed to be somehow self-defined.

Golden Ratio

The most famous among them is known as the golden ratio, sometimes called the golden section or the golden mean. In this ratio the sum of the two values a