Posts Tagged ‘MAA Convergence’

MAA Convergence is both an online journal on the history of mathematics and its use in teaching and an ever-expanding collection of online resources to help its readers teach mathematics using its history. Founded in 2004 by well-known mathematics historians and educators Victor Katz and Frank Swetz, Convergence brings you a variety of interesting articles and teaching tools. It is freely available from the Mathematical Association of America (MAA) website: http://www.maa.org/press/periodicals/convergence

We highlight here some of our newest articles and resources for use in your classroom. Many of them use interactive features to help students understand and explore historical mathematical ideas.

In “Ancient Indian Rope Geometry in the Classroom,” Cynthia Huffman and Scott Thuong offer information, activities, and applets to help you and your students explore the geometry of altar construction in ancient India. In the photograph, boys work on a model of the bird-shaped fire altar in an Agnicayana ritual in Panjal, Kerala, India in 2011. (Photo courtesy of Professor Michio Yano.)

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In “Geometrical Representation of Arithmetic Series,” Gautami Bhowmik explores a geometric tradition in Sanskrit arithmetic texts from Medieval India and shares problems from these texts for your students.

“Historical Activities for the Calculus Classroom,” by Gabriela Sanchis, presents curve-sketching, tangent lines, and optimization in the context of historical problems, and is illustrated by 24 interactive applets and 10 animations.

In “Descartes’ Method for Constructing Roots of Polynomials with ‘Simple’ Curves,” Gary Rubinstein explains and derives Descartes’ methods from his 1637 Geometry and illustrates them using interactive applets. The diagram shows a step in the construction of roots of sixth degree polynomials using a ‘Cartesian parabola’ and circles (from GeoGebra applet by Gary Rubinstein).

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In “Pythagorean Cuts,” Martin Bonsangue and Harris Shultz answer the question ‘Can Euclid’s proof of the Pythagorean Theorem be adapted to shapes other than squares?’ and encourage you to pose it to your students.

“Some Original Sources for Modern Tales of Thales,” by Michael Molinsky, features earliest known sources for stories about Thales, and applets illustrating methods attributed to him. The diagram shows how Thales might have measured the distance from ship to shore (from GeoGebra applet by Michael Molinsky).

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“A GeoGebra Rendition of One of Omar Khayyam’s Solutions for a Cubic Equation,” by Deborah Kent and Milan Sherman, explains and illustrates how the 11th century Persian mathematician, philosopher, and poet geometrically determined a positive real solution to a cubic equation.

“Edmund Halley, 1740” is an historical poem in which Halley reflects on his role in publishing Newton’s Principia, by award-winning Oxford poet Andrew Wynn Owen.

“D’Alembert, Lagrange, and Reduction of Order,” by Sarah Cummings and Adam Parker, offers two historical approaches, one familiar and one unfamiliar, to enrich your differential equations course.

In “Euler and the Bernoullis: Learning by Teaching,” author Paul Bedard reflects on lessons he has learned about mathematics teaching and learning from these great mathematicians.

In “Can You Really Derive Conic Formulae from a Cone?” Gary Stoudt uses 17 interactive applets to explain how attempts to double the cube led ancient Greek mathematicians to discover and develop the conic sections.

Finally our “Index to Mathematical Treasures” includes hundreds of images for use in your classroom, including photographs of “The Cambodian (Khmer) Zero” (of 683 CE) by Amir and Debra Aczel.

See all of these articles and more at MAA Convergence:

http://www.maa.org/press/periodicals/convergence

Join us at the Convergence of mathematics, history, and teaching!

Janet Beery

Editor, MAA Convergence

University of Redlands

(USA)

MAA Convergence is both an online journal on the history of mathematics and its use in teaching and an ever-expanding collection of online resources to help its readers teach mathematics using its history. Founded in 2004 by well-known mathematics historians and educators Victor Katz and Frank Swetz, Convergence brings you a variety of interesting articles and teaching tools. We highlight here some of our newest articles and resources for use in your classroom.
As a web-based publication, Convergence aims to take advantage of new technologies in order to present, explore, and better understand what are often very old ideas. The articles and resources featured here all exemplify this combination of old and new.

(1) “Euclid21: Euclid’s Elements for the 21st Century” introduces a dynamic, interactive version of Euclid’s classic circa 300 BCE geometry text organized via its logical structure.

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Figure 1. Euclid’s first three uses of his Parallel Postulate, as illustrated in Euclid21 (Image from Euclid21 computer application created by Eugene Boman and his student team)
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(2) “Oliver Byrne: The Matisse of Mathematics” offers both the most complete biography of Byrne to date and ideas for using Byrne’s colorful Euclid’s Elements (1847) in the classroom.

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Figure 2. Byrne’s illustration of Euclid’s “windmill” proof of the Pythagorean Theorem. Byrne’s color-coded Euclid was a marvel of Victorian printing and of Pestalozzian pedagogy. (Photo by author Sid Kolpas of his own copy of the book)
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(3) “Bridging the Gap Between Theory and Practice: Astronomical Instruments” shows how your students can design and build armillary spheres, astrolabes, quadrants, sextants, and sundials using such modern technology as 3D printers.

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Figure 3. Student-built sundial from Toke Knudsen’s Ancient Mathematical Astronomy course at SUNY Oneonta (photo by T. Knudsen). See “Bridging the Gap Between Theory and Practice: Astronomical Instruments.”
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(4) “Problems for Journey Through Genius: The Great Theorems of Mathematics” celebrates the popular book’s 25th year in print with downloadable problem sets for each chapter by author William Dunham himself.

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Figure 4. Students can explain how Archimedes wrote the area of an ellipse in terms of the area of a circumscribing circle. (Image created by Janine Stilt)

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(5) In “Pantas’ Cabinet of Mathematical Wonders: Images and the History of Mathematics,” Convergence’s chief treasure-hunter Frank Swetz showcases Convergence’s “Mathematical Treasures,” an ever-growing collection of hundreds of images of historical texts, manuscripts, and objects for classroom use. Search or browse “A Collection of Mathematical Treasures – Index.”

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Figure 5a. A simple but compelling application of the Pythagorean Theorem from Robert Recorde’s Pathway to Knowledge (1551)

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Figure 5b. Caption: Book VI of Euclid’s Elements (originally composed circa 300 BCE) begins with a definition of similar rectilinear figures. This copy of Euclid’s Elements was handwritten on vellum around 1294 CE. (Image courtesy of Columbia University Libraries)
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(6) “Online Museum Collections in the Mathematics Classroom” introduces 27 mathematical object collections from the Smithsonian Institution’s National Museum of American History and offers suggestions for using them with students of all ages.

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Figure 6. Grunow’s circa 1860 spherometer (Photo courtesy of Smithsonian Institution)
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(7) “Jan Hudde’s Second Letter: On Maxima and Minima” contains a translation of the letter and explanation of Hudde’s pre-calculus optimization methods, including an early quotient rule.

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Figure 7. Diagram added by Frans van Schooten when he published Hudde’s “second letter” in 1659. (Image courtesy of ETH-Bibliothek, Zürich, Switzerland)
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(8) “Alan Turing in America” focuses on the important projects in logic and computing Turing worked on during two visits to the U.S.

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Figure 8. This photo of a young Alan Turing is believed to be from 1936-38 when he was at Princeton University. (Photo from Convergence Portrait Gallery)
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See all of these articles and more at MAA Convergence:

http://www.maa.org/publications/periodicals/convergence

Join us at the Convergence of mathematics, history, and teaching!

Janet Beery (USA)
Editor, MAA Convergence
University of Redlands

Founded in 2004 by well-known mathematics historians and educators, Victor Katz and Frank Swetz, Convergence is both an online journal on mathematics history and its use in teaching and an ever-expanding collection of online resources to help its readers teach mathematics using its history.

Convergence is celebrating ten years of publication by continuing to bring you interesting articles and features on the history of grades 8-16 mathematics and exciting ideas and resources for sharing this history with your students.

Articles published this year include:

“Proofs Without Words and Beyond” includes history and philosophy of visual proofs, along with dynamic, interactive “proofs without words 2.0.”

“David Hilbert’s Radio Address” features an audio recording, transcription, and translation into English of Hilbert’s 4-minute radio version of his longer 1930 address with its famous finale, “Wir müssen wissen; wir werden wissen.”

“Cubes, Conic Sections, and Crockett Johnson” shows how author and illustrator Johnson painted his answer to his own question, “What do the straightedge lines and compass arcs do when two parabolas and a hyperbola double a cube, just stand watching?”

“An Investigation of Subtraction Algorithms from the 18th and 19th Centuries” is based on a study of handwritten cyphering books as well as printed arithmetic texts.

We are honoring the best of our ten-year publication history by presenting new, more interactive versions of some of our favorite articles.

“Van Schooten’s Ruler Constructions,” by Ed Sandifer, was among the articles that appeared in the first issue of Convergence in April of 2004.

“Historical Activities for the Calculus Classroom” (2007), by Gabriela Sanchis, consists of three modules that present curve-sketching, tangent lines, and optimization in the context of historical aims and problems, with the aid of 24 interactive applets and 10 animations.

“When Nine Points Are Worth But Eight: Euler’s Resolution of Cramer’s Paradox” (2011), by Rob Bradley and Lee Stemkoski, features a translation of a long lost letter from Euler to Cramer, along with an interactive presentation of Euler’s “elegant example” resolving the paradox.

See all of these articles and more at MAA Convergence:  http://www.maa.org/publications/periodicals/convergence

Convergence is published by the Mathematical Association of America (MAA).

Janet Beery, Editor, MAA Convergence