*Editor:* Janet Beery

*Associate Editors:* Amy Ackerberg-Hastings, Janet 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

### Articles

The Mathematical Cultures of Medieval Europe, by Victor J. Katz

Cultural influences on the mathematics of Islamic, Jewish, and Catholic scholars

Recreational Problems in Medieval Mathematics, by Victor J. Katz

Two problems that endured across time, space, and culture

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 (posted 04/11/18)

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 (posted 04/28/18)

... 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

A Series of Mini-projects from **TR**ansforming **I**nstruction in **U**ndergraduate **M**athematics via **P**rimary **H**istorical **S**ources, 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 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:

- Early Translation of Euclid's
*Elements* into Arabic (1466, original 9th century)
- Fernel's
*De proportionibus* (1528, 4 new images) (posted 05/07/18)
- Koebel's Book on the Astrolabe (1532)
- Apian's
*Folium populi: Instrumentum* (1533)
- Schoener's
*Algorithmus* (1534)
- Peverone's Arithmetic and Geometry (1558, 1581) (posted 04/15/18)
- Ramus's
*Arithmetices *(1586) (posted 04/15/18)
- The
*Trevelyon Miscellany* (1608)
- Oughtred's Key to Mathematics (1631)
- Denis Henrion's
*Use of the Proportional Compass* (1681, 1st ed. 1631)
- Pierre Herigone's
*Cursus Mathematicus* (1644)
- Mydorge's Recreational Mathematics (1639)
- Antoine Arnauld's
*Nouveaux elemens de geometrie *(1667)
- Bachet's Arithmetic of Diophantus (1670) (posted 05/08/18)
- Jean Prestet's
*New Elements of Mathematics *(1694)
- Leonty Magnitsky's
*Arithmetika *(1703)
- Joseph Raphson's
*Analysis equationum universalis *(1702, original 1690)
- William Jones's
*Synopsis Palmariorum Matheseos *(1706)
- Isaac Newton's
*Analysis per quantitatum series, fluxiones ac differentias *(1711)
- Doppelmayr's History of Mathematics in Nuremberg (1730)
- Lamy's
*Mathematical Works* (1734)
- Heilbronner's History of Mathematics (1742)
- Mathematical Lessons or Interviews (Panchaud, 1743)
- Müller's
*Elements of Mathematics* (1765, original 1748)
- Langsdorf on
*Kaestner's Analysis of Finite Quantities* (1776-1777)
- Maria Agnesi’s
*Analytical Institutions* (1801)
- Ludlam's
*Rudiments of Mathematics* (1809, original 1785)
- Legendre's Integral Calculus (1816)
- Simpson's
*A Treatise of Algebra* (1826, original 1745)
- Robert Simson's
*Elements of Euclid* (1834, original 1756)
- De Morgan's
*Elements of Trigonometry and Trigonometrical Analysis* (1837)
- Ramachundra's
*Treatise on Problems of Maxima and Minima Solved by Algebra *(1850)
- Potts's
*Elements of Euclid* (1871, original 1845)
- Sturm’s
* **Cours d’Analyse* (1877, original 1857)
- Chinese Encyclopedia of Mathematics (1882, original 1723)
- Peirce's
* **Linear Associative Algebra* (1882)
- Two Works of Heinrich Weber (1891 and 1895)
- Forsyth's
* Complex Variables *Text (1893)
- Appell and Goursat's
* Analysis *(1895)
- Burkhardt on Analytic Functions (1897)
- Snyder and Hutchinson's
* **Differential and Integral Calculus* (1902)
- Goursat's
* Calculus Classic *(1904, original 1902)
- Wilson's
* **Solid Geometry and Conic Sections* (1908, original 1872)
- Hadamard's
* Calculus of Variations *(1910)* *
- Fubini's
* Analysis *(1920, original 1913)
- Hobson's
* **Theory of Functions of a Real Variable* (1921, original 1907)
- Hardy's
* **A Course in Pure Mathematics* (1921, original 1908)
- Oswald Veblen’s
* **Analysis Situs* (1922)
- Lamb's
* **An Elementary Course of Infinitesimal Calculus* (1934, original 1897)
- Sophus Lie’s
* Collected Papers *(1934)