The Mathematics of Everyday Life

In the book, The Mathematics of Everyday Life, Alfred S. Posamentier and Christian Spreitzer have brought out the drill and practice and, what seems, endless calculations in mathematics, to how relevant mathematics is in everyday life.  By exploring various different fields; algebra, number theory, geometry, and probability, the book presents to the reader how and why mathematics is deeply rooted in almost every aspect of our lives.  The books help one give a further appreciation in the world we live in. From knowing basic geometry, the reader will discover the optimal point on a soccer field from which to shoot a goal, understanding the “whispering effect” inside the Capitol rotunda, the mathematics in art, and the artistic version of the Möbius strip is used to symbolize recycling.  The reader will obtain a new perspective of the elegance of mathematics and how mathematics explains everyday experiences and observations.

As pointed out in the introduction, Posamentier and Spreitzer's motivation to write this book was to help the reader think outside set curriculums.  At the high school level, much emphasis is placed on teaching a curriculum that is mandated by administrators and various state education boards with little to no room for deviating from a set schedule to further enhance the student’s mathematics experience.  There is a mentality to “teach to the test” especially with state testing. While topics must be covered, as they are essential for mathematics and other STEM fields, the book provides students topics and ideas that may not be covered in the classroom.

While reading the book, I had to stop and think about certain topics.  For example, on pages 34-35, the authors discuss Roman Numerals and the Super Bowl 50, which took place in February 2016.  In that year, the traditional Roman Numerals were not used (I never thought about this and never bothered to notice while watching the game that year).  The Roman Numeral for 50 is L and the NFL didn’t use L since it would be difficult to design an aesthetically pleasing logo for “Super Bowl L.” On page 48, there is an example of how certain peculiarities can be viewed.  A random month and year are chosen, October 2019 and Table 1.7 blocks off a 3 x 3 array of dates. Adding 8 to the smallest number (9) and multiplying that sum by 9 to get (9 + 8) * 9 = 153. Multiplying the sum of the numbers in the middle row, which is 51, of the shaded matrix by 3, we obtain 153 – this is due to the fact that the sum of the numbers in the middle column is 1/3 of the sum of the nine numbers.  Another interesting way to look at numbers, among many presented in the book, are numbers of terminal digit 5. Pages 69-71 discuss the 3-step process of squaring 45 = 2025. The following pattern is presented:

\( 05^{2} = 25 \), \( 15^{2}2 = 225 \), \( 25^{2} = 625 \), \( 35^{2} = 1225 \) , \( 45^{2} = 2025 \), \( 55^{2} = 3025 \), \( 65^{2} = 4225 \), \( 75^{2} = 5625 \), \( 85^{2} = 7225 \), \( 95^{2} = 9025 \)

Each number ends in 25 and the preceding digits are obtained as follows:

\( 05^{2} = 0025, 0 = 0 * 1 \)

\( 15^{2} = 0225, 2 = 1 * 2 \)

\( 25^{2} = 0625, 6 = 2 * 3 \)

\( 35^{2} = 1225, 12 = 3 * 4 \)

\( 45^{2} = 2025, 20 = 4 * 5 \)

\( 55^{2} = 3025, 30 = 5 * 6 \)

\( 65^{2} = 4225, 42 = 6 * 7 \)

\( 75^{2} = 5625, 56 = 7 * 8 \)

\( 85^{2} = 7225, 72 = 8 * 9 \)

\( 95^{2} = 9025, 90 = 9 * 10 \)

Pages 142-150 discuss playing cards, the mathematics of poker, and probability.  After the problem on page 143 is presented, the question to be addressed is what is the probability that at least one pair being turned over will be identical?  The probability the first two cards don’t match is 1 – 1/52 and thus, the probability that none of the 52 cards turned over in pairs produced a match is the product (1 – (1/52))52.  This reminds us of (1 + (1/n))n.  As n tends to infinity, we get e.  Pages 201-206 discusses how to play billiards using a mirror against the side cushion and aiming the cue ball at the mirror, shooting it to the point at which the target ball is seen in the mirror.  Pages 319-322 talk about clocks with the key question: At what time (exactly) will the hands of a clock overlap after 4:00?

This book offers a deep and rich understanding of how mathematics is all around us.  The examples are diverse and are too many to list in a review. I can see this book as a motivational book for those students who love mathematics at an early age, perhaps at the high school level, to gain more insight on how mathematics is used in our daily routines, activities, and observations.  I have always loved numbers and this book now holds a special place in my personal library.  I’m sure it will hold a special place in yours and in your heart.

Peter Olszewski is a Mathematics Lecturer at The Pennsylvania State University, The Behrend College. His Research fields are in mathematics education, Cayley Color Graphs, Markov Chains, and mathematical textbooks. He can be reached at pto2@psu.edu. Webpage: www.personal.psu.edu/pto2. Outside of teaching and textbook editing, he enjoys playing golf, playing guitar and bass, reading, gardening, traveling, and painting landscapes.