Tuesday, October 12, 2010

Exploring the World of Mathematics by John Hudson Tiner

book cover

Exploring the World of Mathematics
by John Hudson Tiner

ISBN-13: 978-0890514122
Paperback: 160 pages
Publisher: Master Books
Released: June 2004, Nov. 2005

Source: Bought from local bookstore.

Book Description from Back Cover:
Numbers surround us. Just try to make it through a day without using any. It’s impossible: telephone numbers, calendars, volume settings, shoe sizes, speed limits, weights, street numbers, microwave timers, TV channels, and the list goes on and on. The many advancements and branches of mathematics were developed through the centuries as people encountered problems and relied upon math to solve them. For instance:

  • What timely invention was tampered with by the Caesars and almost perfected by a pope?

  • Why did ten days vanish in September of 1752?

  • How did Queen Victoria shorten the Sunday sermons at chapel?

  • What important invention caused the world to be divided into time zones?

  • What simple math problem caused the Mars Climate Orbiter to burn up in the Martian atmosphere?

  • What common unit of measurement was originally based on the distance from the equator to the North Pole?

  • Does water always boil at 212° Fahrenheit?

  • What do Da Vinci’s Last Supper and the Parthenon have in common?

  • Why is a computer glitch called a “bug”?

It’s amazing how ten simple digits can be used in an endless number of ways to benefit man. The development of these ten digits and their many uses is the fascinating story you hold in your hands: Exploring the World of Mathematics.

Exploring the World of Mathematics is a history of the development of mathematics with some instruction on how to do the various types of math worked in. (Chapters 5, 9, and 10 were more focused on math instruction than history.)

The text was engaging and easy to understand. Much of the book was suitable for middle schoolers, though some chapters were more high school level. There were useful black and white charts and illustrations. At the end of each chapter, there were 10 questions--most tested if you learned the important points in the chapter, but some were math problems based on what was learned. The answers were in the back.

The book occasionally referred to things in the Bible, like explaining the cubit as an ancient measurement of length. The author had math start with the ancient Egyptians (since, according to him, it wasn't needed before then because people were roaming herders). It also referred to a Sumerian counting system that started back in 3300 B.C.

Overall, the book was interesting and well-written. I'd recommend it to those interested in an overview of the development of mathematics or to those desiring to teach their children math in an interesting way.

Chapter 1 talked about ancient calendars (how days, months, and years were calculated in various cultures) and how the modern calendar was developed. Chapter 2 talked about marking the passage of time (including how & why people started counting hours, minutes, and seconds). Chapter 3 talked about the development of weights and measures from ancient ones to modern non-metric systems. Chapter 4 talked about the development of the metric system (mostly weight, length, capacity, and temperature).

Chapter 5 talked about how ancient Egyptians used basic geometry to build pyramids and survey farm land. Chapter 6 talked about how ancient Greeks continued to develop mathematics. Chapter 7 talked about the different systems and symbols for numbers in various cultures and times. Chapter 8 talked about number patterns (like odd, even, prime, Fibonacci numbers, square numbers, and triangular numbers).

Chapter 9 talked about mathematical proofs, decimal points, fractions, negative numbers, irrational numbers, and never-ending numbers. Chapter 10 talked about algebra and analytical geometry. Chapter 11 talked about network design, combinations & permutations, factorials, Pascal's triangle, and probability. Chapter 12 talked about the development of counting machines, from early mechanical calculators to modern digital calculators. Chapter 13 talked about the development of modern computers. Chapter 14 gave some math tricks and puzzles.

If you've read this book, what do you think about it? I'd be honored if you wrote your own opinion of the book in the comments.

Excerpt from page 9
Most names for months in our calendar are from the Roman calendar. The ancient Roman calendar originally had only 10 months and 304 days. The year began with the month of March. Later, the months of January and February were inserted before March, and the new year began with January.

January was named for Janus. In Roman mythology, he was the keeper of doorways. January was the entrance to the new year. February was from a Roman word meaning "festival." March was named after Mars, the Roman god of war. April came from a Roman word meaning "to open," probably because buds opened in April. May was named after Maia, the mother of Mercury. June was named after Juno, the queen of the gods in Roman mythology. She was portrayed as the protector of women.

In the Roman calendar, months after June had names based on their original calendar before January and February were added: Quintilis (quin, "fifth"), Sextilis (sex, "sixth"), September (sep, "seventh"), October (oct, "eighth"), November (non, "ninth"), and December (dec, "tenth").

Julius Caesar took the month Quintilis and named it July after himself. The next Roman ruler, Augustus Caesar, took the month Sextilis and named it August after himself.

August had only 30 days but July had 31 days. Augustus took another day from February and added it to August so his month would be as long as the one for Julius Caesar.

Read chapter one.

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