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What's in Convergence? - Contents of Volume 15 - 2018

Editor:  Janet Beery

Associate Editors: Amy Ackerberg-Hastings, Janet Heine Barnett, Maureen Carroll, Lawrence D'Antonio, Victor Katz, Michael Molinsky, Elyn Rykken, Randy Schwartz, Amy Shell-Gellasch, Jody Sorensen, Gary Stoudt, Erik R. Tou

Founding Editors: Victor Katz, Frank Swetz


Historical Reflections on Teaching Trigonometry, by David M. Bressoud The functional approach of circle trigonometry is the historical approach!

Crossword Puzzle: Mathematical Potpourri, by Sid Kolpas and Stu Ockman Our second puzzle from a mathematics professor and a NY Times crossword puzzle constructor!

Descriptions of the Integer Number Line in United States School Mathematics in the 19th Century, by Nicole M. Wessman-Enzinger Gradual development of the now ubiquitous number line traced through textbooks of the time.

Russian Multiplication, Microprocessors, and Leibniz, by Sid Kolpas A traditional method of multiplication via binary arithmetic finds a modern use.

A Writing Intensive General Education History of Mathematics Course, by Amy Shell-Gellasch ... for students who think they aren't good at or don't like mathematics!

More Classroom Activities Based on Ancient Indian Rope Geometry, by Cynthia J. Huffman and Scott V. Thuong Activities, applets, and information to help students explore the geometry of altar construction in ancient India.

HOM SIGMAA 2018 Student Paper Contest Winners Read the winning entry, "Race to Refraction: The Repeated Discovery of Snell's Law," along with the two runners-up.

Divisibility Tests: A History and User's Guide, by Eric L. McDowell Discoveries, rediscoveries, and generalizations of these tests to pique students' interest.

Elementary Soroban Arithmetic Techniques in Edo Period Japan, by Rosalie Joan Hosking, Tsukane Ogawa, and Mitsuo Morimoto Learn to solve problems from the Taisei Sankei (c. 1700) on the Japanese abacus.

The Root of the Matter: Approximating Roots with the Greeks, by Matthew Haines and Jody Sorensen The ancient method of Theon's Ladder has both geometric and matrix interpretations.

Cuisenaire Art: Modeling Figurate Number Sequences and Gnomonic Structures in a History of Mathematics Classroom, by Günhan Caglayan Students construct Cuisenaire rod models per instructions from Theon and Nicomachus.

Mathematical Treasures of Japan in the Edo Period, by Frank J. Swetz Twelve distinct works illustrate the range of mathematics produced in Japan from 1603 to 1867.

Billingsley's Sources for the First English Euclid's Elements: Two Annotated Mathematical Treasures, by Frank J. Swetz A Greek source and a Latin source annotated by the translator in the mid-16th century now reside in Princeton, New Jersey.

The Ladies' Diary: A True Mathematical Treasure, by Frank J. Swetz An 18th century almanac for "ladies" became a source for mathematical problems and solutions.

On Squares, Rectangles, and Square Roots, by María Burgos and Pablo Beltrán-Pellicer Sixth-graders extract square roots using manipulatives and a method from ancient China.

An Arabic Finger-reckoning Rule Appropriated for Proofs in Algebra, by Jeffrey A. Oaks In a 1301 work, Ibn al-Bannāʾ based his proofs on a common mental multiplication technique.

John Napier's Binary Chessboard Calculator, by Sidney J. Kolpas and Erwin Tomash Napier's lesser known invention: a 5-function calculator via binary arithmetic on a chessboard.

A Classic from China: The Nine Chapters, by Randy K. Schwartz History of and problems for students from this early and influential Chinese work.

Ongoing Series

A Series of Mini-projects from TRansforming Instruction in Undergraduate Mathematics via Primary Historical Sources, by Janet Barnett, Kathy Clark, Dominic Klyve, Jerry Lodder, Danny Otero, Nick Scoville, and Diana White

Math Origins, by Erik R. Tou How were concepts, definitions, and theorems familiar to today's students of mathematics developed over time?

Mathematical Treasures

Mathematical Treasures at the Linda Hall Library, by Cynthia J. Huffman Description of the physical and digital history of science collections of the Linda Hall Library in Kansas City. At least 75 of LHL's digitized rare books relate to the history of mathematics and can be used in classrooms.

Mathematical Treasures from the Linda Hall Library added during 2018:

Mathematical Treasures, by Frank J. Swetz

Index to Mathematical Treasures Collection: Images of historical texts and objects from libraries, museums, and individuals around the world for use in your classroom!

Mathematical Treasures added during 2018:

"What's in Convergence? - Contents of Volume 15 - 2018," Convergence (December 2017)