Brings to life many of the characters who played a role in the development of the Pythagorean theorem--from the ancient Babylonians and Pythagoras to Albert Einstein and modern-day mathematicians--in a history that provides a fascinating backdrop to an enduring mathematical legacy.
Thales, Pythagoras, Engineering, Diagrams, and the Construction of the Cosmos out of Right Triangles
Author: Robert Hahn
Pubpsher: SUNY Press
Explores Thales’s speculative philosophy through a study of geometrical diagrams. Bringing together geometry and philosophy, this book undertakes a strikingly original study of the origins and significance of the Pythagorean theorem. Thales, whom Aristotle called the first philosopher and who was an older contemporary of Pythagoras, posited the principle of a unity from which all things come, and back into which they return upon dissolution. He held that all appearances are only alterations of this basic unity and there can be no change in the cosmos. Such an account requires some fundamental geometric figure out of which appearances are structured. Robert Hahn argues that Thales came to the conclusion that it was the right triangle: by recombination and repackaging, all alterations can be explained from that figure. This idea is central to what the discovery of the Pythagorean theorem could have meant to Thales and Pythagoras in the sixth century BCE. With more than two hundred illustrations and figures, Hahn provides a series of geometric proofs for this lost narrative, tracing it from Thales to Pythagoras and the Pythagoreans who followed, and then finally to Plato’s Timaeus. Uncovering the philosophical motivation behind the discovery of the theorem, Hahn’s book will enrich the study of ancient philosophy and mathematics alike.
entertaining and informative book, veteran math educator Alfred S. Posamentier makes the importance of the Pythagorean Theorem delightfully clear. Posamentier begins with a brief history of Pythagoras himself and the early use of his theorem by the ancient Egyptians, Babylonians, Indians, and Chinese, who used it intuitively long before Pythagoras's name was attached to it. Following this introduction to the topic, he shows the many ingenious ways in which the theorem has been proved visually by using highly imaginative diagrams. Some of these go back to ancient mathematicians; others are comparatively recent proofs, including one by the twentieth president of the United States, James A. Garfield. After demonstrating some curious applications of the theorem, Posamentier then explores the Pythagorean triples, pointing out the many hidden surprises of the three numbers that can represent the sides of a right triangle (e.g., 3, 4, 5 and 5, 12, 13). The relationships --
The Pythagorean Theorem for Babies is intended to introduce babies to the principles of the Pythagorean Theorem, and also provides a colorful proof of the theorem. Mathematician Fred Carlson believes that it's never too early to introduce children, and even babies, to the basic concepts of advanced mathematics. He is sure that after reading this book, the second in his Mathematics for Babies series, you will agree with him! If you like this book, please also check out "Non-Euclidean Geometry for Babies"!
An exploration of one of the most celebrated and well-known theorems in mathematics By any measure, the Pythagorean theorem is the most famous statement in all of mathematics. In this book, Eli Maor reveals the full story of this ubiquitous geometric theorem. Although attributed to Pythagoras, the theorem was known to the Babylonians more than a thousand years earlier. Pythagoras may have been the first to prove it, but his proof—if indeed he had one—is lost to us. The theorem itself, however, is central to almost every branch of science, pure or applied. Maor brings to life many of the characters that played a role in its history, providing a fascinating backdrop to perhaps our oldest enduring mathematical legacy.
Pythagoras, a famous Greek scholar, sathematician, and philosopher, formulated a proof for a theorem that is named for him—the Pythagorean theorem. This theorem states that in any right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. The Pythagorean theorem for right-angled triangles likely was known long before the time of Pythagoras. It was probably used by the ancient Egyptians to construct the pyramids. The theorem is quite believable without rigorous proof to anyone willing to expend a modest effort in some experimentation. One method is to draw a number of right-angled triangles in as wide a variety as practicable and measure all of the sides. It will be determined that, for each triangle drawn, the square of the length of the side opposite the right angle is about equal to the sum of the lengths of the squares of the other two sides. Another method requires the availability of a balance. For this more interesting experiment, construct a right-angled triangle and a square on each side using a piece of sheet metal or cardboard. Then cut out the three squares and weigh them on the balance. The square on the hypotenuse should balance the other two. Contained within this book are some rigorous proofs and some interesting perspectives regarding right angles and right-angled triangles. Doubtless, this theorem is one of the most useful concepts in mathematics.
The Pythagorean Theorem is one of the most important ideas in all of mathematics. In this book, students study history and geometry as they explore eight elegant proofs of the theorem from across the centuries. Included are interesting facts about the theorem, a brief biography of Pythagoras, and a list of concepts needed to understand the proofs. Learn how Leonardo Da Vinci, President James A. Garfield, Pythagoras, the Chinese, Bhaskara, and others proved this famous theorem about the right triangle. This would be a useful book for any student taking Geometry, or anyone interested in Mathematics History. NOW WITH A LINK TO POWERPOINT SLIDES YOU CAN DOWNLOAD WITH ANIMATIONS, VIDEOS, PICTURES, AND HYPERLINKS TO SUPPLEMENT THE BOOK. Each proof is displayed in color with an explanation of the steps taken in its geometric presentation. Blackline masters for the proofs, and for manipulatives that offer students hands-on understanding, are included. The book is in PDF format.
Aligns to CCSS 8.G.B.7: Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
Pubpsher: Lorenz Educational Press
Fill in the gaps of your Common Core curriculum! Each ePacket has reproducible worksheets with questions, problems, or activities that correspond to the packet’s Common Core standard. Download and print the worksheets for your students to complete. Then, use the answer key at the end of the document to evaluate their progress. Look at the product code on each worksheet to discover which of our many books it came from and build your teaching library! This ePacket has 8 activities that you can use to reinforce the standard CCSS 8.G.B.7: Applying the Pythagorean Theorem. To view the ePacket, you must have Adobe Reader installed. You can install it by going to http://get.adobe.com/reader/.
Engage your mathematics students at the beginning of class with this whole-class warm-up activity. This product features a step-by-step lesson, assessment information, and a snapshot of what the warm-up looks like in the classroom.