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Exploring
Exploring the World of Mathematics: From Ancient Record Keeping to the Latest Advances in Computers (Exploring (New Leaf Press))
Numbers surround us. Just try to make it through a day without using any. It’s 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 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 Exploring the World of Mathematics.
- GenresNonfictionMathematics
157 pages, Paperback
First published January 1, 2004
10 people are currently reading
65 people want to read
About the author
John Hudson Tiner
102 books17 followersJohn Hudson Tiner is a lifelong educator, and has acquired a reputation for writing clearly about science. He has wide-ranging interests, and has also written about American history and several of the sciences. He and his wife, Jeanene, live in Missouri.
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Displaying 1 - 7 of 7 reviews
May 16, 2024
33% fascinating
33% practical
34% dead boring
I agree with another reviewer that this book tries to do too much.
It just missed the mark in several areas.
My least favorite of the Tiber’s thus far.
Still a worthwhile series…
33% practical
34% dead boring
I agree with another reviewer that this book tries to do too much.
It just missed the mark in several areas.
My least favorite of the Tiber’s thus far.
Still a worthwhile series…
August 17, 2021
The best Math/Science book I've ever read.
April 30, 2012
This book is part of a series by Tiner "Exploring the world of ..."; others are on Medicine, Planet Earth, Chemistry, Physics and The World Around You. The book is obviously written for the Christian market and the American market.
In a sense this book aims to do too much. It covers a wide historical period and a wide range of mathematical concepts for 'students of several different ages and skill levels'.
Tiner starts off by looking at measuring the years and then the hours. Measurement is dependent upon number, so I would have thought a better first place to start would be the numerical aspect but that isn't dealt with until chapter 7.
There are one or two math errors: eg 'Every time a number is multiplied by 1,000, three zeros are added, and a new name is given'. Not if the number is 1.3! Such an approach destroys place value concepts - not a great idea in an introductory maths book!
Bible verses are interspersed - sometimes without apparent reason. This approach tends to view Christianity as an icing on the mathematics cake. There are side boxes on topics such as Hebrew and Jewish Calandar of the Old Testament and Cubit in the Bible. Peter's catch of 153 fish (Jn 21:11) is examined - 153 = 1^3 + 5^3 + 3^3. However, little attempt is made to fully integrate Christianity and mathematics.
There are a number of missed opportunities. For example, on the decimal system, Tiner applauds the United States for being the first country to adopt a decimal money system and showed its advantages and yet they haven't embraced full metrification - it would have been interesting to have explored why not. And in the context of decimals how are we, in light of a Christian worldview, to interpret Tobias Dantzig's assertion in Number The Language of Science (1930):
... man counts by tens, his ten fingers will remind him of the human origin of this most important phase of his mental life. So may the decimal system stand as a living monument to the proposition: Man is the measure of all things."
There is a helpful discussion on the Golden ratio - Tiner noted that the dimensions of Noah's Ark in (Gn 6:15) and the Ark of the Covenant are close to the Golden ratio; but why is 1.618 so prevalent in creation?
Pythagras' absolutisation of number and the Greek rationalisation of proof are not really explored - this would have been a good opportunity to show how worldviews shape mathematics.
The Christian faith of mathematicians is also largely absent. Some mathematicians who are Christians are mentioned, but little is made of their faith and in the portrayal of Newton one could be forgiven for thinking that Newton was an orthodox evangelical rather than a unitarian.
I have perhaps been a little over critical; and it is undoubtably much better than the Christian maths book I haven't written!! There is much of use in this book and it may provide the Christian teacher with some useful ideas. It is well laid out and illustrated with line drawings and photographs. It would make for a good resource for the school library or Christian teacher.
In a sense this book aims to do too much. It covers a wide historical period and a wide range of mathematical concepts for 'students of several different ages and skill levels'.
Tiner starts off by looking at measuring the years and then the hours. Measurement is dependent upon number, so I would have thought a better first place to start would be the numerical aspect but that isn't dealt with until chapter 7.
There are one or two math errors: eg 'Every time a number is multiplied by 1,000, three zeros are added, and a new name is given'. Not if the number is 1.3! Such an approach destroys place value concepts - not a great idea in an introductory maths book!
Bible verses are interspersed - sometimes without apparent reason. This approach tends to view Christianity as an icing on the mathematics cake. There are side boxes on topics such as Hebrew and Jewish Calandar of the Old Testament and Cubit in the Bible. Peter's catch of 153 fish (Jn 21:11) is examined - 153 = 1^3 + 5^3 + 3^3. However, little attempt is made to fully integrate Christianity and mathematics.
There are a number of missed opportunities. For example, on the decimal system, Tiner applauds the United States for being the first country to adopt a decimal money system and showed its advantages and yet they haven't embraced full metrification - it would have been interesting to have explored why not. And in the context of decimals how are we, in light of a Christian worldview, to interpret Tobias Dantzig's assertion in Number The Language of Science (1930):
... man counts by tens, his ten fingers will remind him of the human origin of this most important phase of his mental life. So may the decimal system stand as a living monument to the proposition: Man is the measure of all things."
There is a helpful discussion on the Golden ratio - Tiner noted that the dimensions of Noah's Ark in (Gn 6:15) and the Ark of the Covenant are close to the Golden ratio; but why is 1.618 so prevalent in creation?
Pythagras' absolutisation of number and the Greek rationalisation of proof are not really explored - this would have been a good opportunity to show how worldviews shape mathematics.
The Christian faith of mathematicians is also largely absent. Some mathematicians who are Christians are mentioned, but little is made of their faith and in the portrayal of Newton one could be forgiven for thinking that Newton was an orthodox evangelical rather than a unitarian.
I have perhaps been a little over critical; and it is undoubtably much better than the Christian maths book I haven't written!! There is much of use in this book and it may provide the Christian teacher with some useful ideas. It is well laid out and illustrated with line drawings and photographs. It would make for a good resource for the school library or Christian teacher.
October 11, 2010
"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.
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.
September 4, 2013
Mathematics. Who ever knew they could be so fascinating? This book was written not only with mathematics in view, but history. History is one subject that has always fascinated me, and John Tiner Hudson actually managed to rope me into enjoying a text of mathematical equations by how he presented the material!
Some of the topics I especially enjoyed were:
The history of the calendar and seasons. Here, the author explores the mathematics behind our calendar. Almost everyone knows about the Gregorian and the Julian calendar, but did you know that the math that is required to set us on the right track with our current calendar is still just a little bit off? I didn't, but in a couple hundred years we will have to adjust it or our days won't line up!
The largeness of numbers. Kids (and adults!) are always fascinated by this one. Wondering what the largest number is? It's a googolplexian! It is the number one followed by a googolplex of zeros. Of course, also included in the section is who and how this name came to be!
Great historical math geniuses, including Archimedes, Galileo, Kepler, Newton etc., are covered in detail and many of the problems that they solved or attempted to solve were included. Throughout the book, puzzles such as magic cubes and the seven Königsberg bridges are detailed out and students will very much enjoy looking through the formulas and attempting to solve these famous puzzles themselves.
John Tiner Hudson has created a fantastic resource for parents. This is THE perfect supplemental material. He has managed to create a fantastic read that is easy enough for a fifth grader to understand, but with enough data for a middle or high school student to benefit from. The author has further aided the usability of the book by including text problems at the end of the chapter as well as working through problems "real time" right in the text for the student. I would say most of the actual problems would be intended for a the higher end of student, but a fifth or sixth grader could probably manage with some help. A younger student could certainly read the text and treat the questions as optional. The chapters are short, but detailed, the problems and data is presented in an interesting way. In short, I highly recommend this book.
*Thanks to Master Books for providing a complimentary copy in exchange for my honest review.
Some of the topics I especially enjoyed were:
The history of the calendar and seasons. Here, the author explores the mathematics behind our calendar. Almost everyone knows about the Gregorian and the Julian calendar, but did you know that the math that is required to set us on the right track with our current calendar is still just a little bit off? I didn't, but in a couple hundred years we will have to adjust it or our days won't line up!
The largeness of numbers. Kids (and adults!) are always fascinated by this one. Wondering what the largest number is? It's a googolplexian! It is the number one followed by a googolplex of zeros. Of course, also included in the section is who and how this name came to be!
Great historical math geniuses, including Archimedes, Galileo, Kepler, Newton etc., are covered in detail and many of the problems that they solved or attempted to solve were included. Throughout the book, puzzles such as magic cubes and the seven Königsberg bridges are detailed out and students will very much enjoy looking through the formulas and attempting to solve these famous puzzles themselves.
John Tiner Hudson has created a fantastic resource for parents. This is THE perfect supplemental material. He has managed to create a fantastic read that is easy enough for a fifth grader to understand, but with enough data for a middle or high school student to benefit from. The author has further aided the usability of the book by including text problems at the end of the chapter as well as working through problems "real time" right in the text for the student. I would say most of the actual problems would be intended for a the higher end of student, but a fifth or sixth grader could probably manage with some help. A younger student could certainly read the text and treat the questions as optional. The chapters are short, but detailed, the problems and data is presented in an interesting way. In short, I highly recommend this book.
*Thanks to Master Books for providing a complimentary copy in exchange for my honest review.
November 23, 2010
Educational book that the boys and I read together. It was fun and interesting. Most was at a middle school level, but some at a high school level. If you like patterns or puzzles, you will like this history of mathematics.
September 4, 2014
Really like this one so far. It's interesting to read and keeps my attention even as an adult.
Displaying 1 - 7 of 7 reviews