Grandpa, Tell Us About Phi, the Golden Number: Explore the amazing connection between nature and math!

This is a book for people from 9 to 90 who like surprises. And beauty. My intention is to show the beauty in both nature and mathematics, with some surprising connections that will make you stop and think. This book is particularly valuable for homeschooling, including exploratory projects for the students. With this and future books, I want to foster curiosity, particularly in young people who might now see beyond boring or dull school subjects into a new world of science, physics, engineering, and math.In this book, Grandpa and his grandchildren embark on an adventure into the fascinating connection between nature and a number called phi (ϕ). Phi is also called the Golden Number, the Golden Ratio, the Golden Section, and the Divine Proportion. It is an irrational number, like pi (π), and its value is approximately 1.618. One of the interesting facts about phi is its relationship to the famous Fibonacci series and to the beautiful logarithmic spiral, one of the most beautiful shapes in nature. Grandpa and the children find Fibonacci numbers in the numbers of flower petals, the number of spirals on pine cones and pineapples, the shape of seashells, the genealogy of bees, how falcons attack their prey, the shape of soccer balls, and more. From the structure of a carbon crystal, to the spiral one sees in distant galaxies, phi is pervasive throughout nature. And over recorded history, it has had an effect on science, religion, astronomy, mathematics, art, and architecture.I hope that this book results in a few young people realizing that the wonders of nature and mathematics are worth more exploration and that because of that, our society gains a few good engineers, physicists, and natural scientists.