## ‘A Dynamical Form of Mechanical Effect’: Thomson's Thermodynamics

in** Kelvin: Life, Labours and Legacy**

April 2008; p ublished online May 2008 .

Chapter. Subjects: History of Mathematics. 7791 words.

As he settled into his position as Professor of Natural Philosophy at Glasgow, Thomson would spend much of his time over the subsequent years pondering over the problem of heat and the...

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## The ACE and the shaping of British computing

in** Alan Turing's Automatic Computing Engine**

April 2005; p ublished online January 2008 .

Chapter. Subjects: History of Mathematics. 8370 words.

This chapter focuses on the legacy of the ACE to British computing. Design of the ACE began in earnest in 1953, when the pilot machine was complete, although physical construction did not...

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##
*The ACE Simulator and the Cybernetic Model*

in** Alan Turing's Automatic Computing Engine**

April 2005; p ublished online January 2008 .

Chapter. Subjects: History of Mathematics. 1570 words.

This chapter discusses the ACE simulator and the Cybernetic Model. The ACE simulator was a demonstration machine built as an aid to the visualization of binary operations. Designed by D. W....

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## The ACE Test Assembly, the Pilot ACE, the Big ACE, and the Bendix G15

in** Alan Turing's Automatic Computing Engine**

April 2005; p ublished online January 2008 .

Chapter. Subjects: History of Mathematics. 4604 words.

This chapter begins with a brief discussion of the ENIAC and the EDVAC projects in the US. The author then describes his work at the National Physical Laboratory. Topics covered include the...

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## Adventures of the Diagonal: Non-Euclidean Mathematics and Narrative

in** Circles Disturbed**

March 2012; p ublished online October 2017 .

Chapter. Subjects: History of Mathematics. 15150 words.

This chapter explores the relationship between narrative and non-Euclidean mathematics. It considers how non-Euclidean mathematics and the narratives accompanying it are linked: first, to...

## The age of debates

in** Heavenly Numbers**

November 2017; p ublished online January 2018 .

Chapter. Subjects: History of Mathematics. 14488 words.

In this chapter, we look at a further aspect of the story revealed by the documents collected by Cai Yong and Liu Hong: the records of debates on technical matters during the first and...

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## Alan Turing's Automatic Computing Engine

April 2005; p ublished online January 2008 .

Book. Subjects: History of Mathematics. 576 pages.

The mathematical genius Alan Turing (1912-1954) was one of the greatest scientists and thinkers of the 20th century. Now well known for his crucial wartime role in breaking the ENIGMA code,...

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## Algebra

in** The Mathematical World of Charles L. Dodgson (Lewis Carroll)**

February 2019; p ublished online April 2019 .

Chapter. Subjects: History of Mathematics. 8585 words.

This chapter is concerned with a single textbook written by Dodgson in 1867—An *Elementary Treatise on Determinants*. His book concerned the study of determinants, an algebraic construct that...

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## Algebraic Thought in Ancient and Medieval China

in** Taming the Unknown**

July 2014; p ublished online October 2017 .

Chapter. Subjects: History of Mathematics. 9111 words.

This chapter takes a look at the scope of mathematics in Ancient and Medieval China. Although the Chinese engaged in numerical calculation as early as the middle of the second millennium...

## Algebraic Thought in Medieval India

in** Taming the Unknown**

July 2014; p ublished online October 2017 .

Chapter. Subjects: History of Mathematics. 10163 words.

This chapter explores medieval Indian algebraic thought in the works of Āryabhạta, author of the astronomical treatise *Āryabhạtīya* (ca. 500 CE), and Brahmagupta, who wrote the *Brāhma-sp...*

## Algebraic Thought in Medieval Islam

in** Taming the Unknown**

July 2014; p ublished online October 2017 .

Chapter. Subjects: History of Mathematics. 15366 words.

This chapter turns to the realm of Islamic mathematics, which lasted longer than both the era of classical Greek mathematics and the age of “modern mathematics.” In the Islamic world,...

## Amsterdam, Breda, 1643–1652

in** John Pell (1611-1685) and His Correspondence with Sir Charles Cavendish**

November 2004; p ublished online September 2007 .

Chapter. Subjects: History of Mathematics. 20291 words.

This chapter chronicles the life of John Pell in Amsterdam and Breda from 1643 to 1652. John Pell had little idea of what awaited him in Amsterdam; apparently he thought his trip was to be...

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## Analysis of Crossword Puzzle Difficulty Using a Random Graph Process

in** The Mathematics of Various Entertaining Subjects**

December 2015; p ublished online October 2017 .

Chapter. Subjects: History of Mathematics. 9104 words.

This chapter quantifies the dynamics of a crossword puzzle by using a network structure to model it. Specifically, the chapter determines how the interaction between the structure of cells...

## The Ancient Approach

in** Heavenly Mathematics**

April 2017; p ublished online May 2018 .

Chapter. Subjects: History of Mathematics. 4978 words.

This chapter discusses the ancient approach to trigonometry, beginning with Hipparchus of Rhodes, the founder of trigonometry. It reconstructs when and where Hipparchus must have lived by...

## The Ancient Greek World

in** Taming the Unknown**

July 2014; p ublished online October 2017 .

Chapter. Subjects: History of Mathematics. 7587 words.

This chapter focuses on the mathematicians of Ancient Greece; more specifically, on the elements of geometrical algebra present in the works of Euclid and Apollonius, as well as the...

## Applications of the Pilot ACE and the DEUCE

in** Alan Turing's Automatic Computing Engine**

April 2005; p ublished online January 2008 .

Chapter. Subjects: History of Mathematics. 5542 words.

This chapter discusses applications of the Pilot ACE. These applications include linear equations, photogrammetry, traffic simulation, matrix programmes, demonstration programmes, and...

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## The Arab Gift

in** Enlightening Symbols**

December 2016; p ublished online January 2018 .

Chapter. Subjects: History of Mathematics. 1051 words.

This chapter focuses on the Arabs' contributions to the modern number system. It first considers the role played by Abu Jafar Muhammad ibn Musa al-Khwārizmī, the greatest Arab mathematician...

## Areas, Angles, and Polyhedra

in** Heavenly Mathematics**

April 2017; p ublished online May 2018 .

Chapter. Subjects: History of Mathematics. 5295 words.

This chapter explains how to find the area of an angle or polyhedron. It begins with a discussion of how to determine the area of a spherical triangle or polygon. The formula for the area...

## Ariadne's thread: William Oughtred's Clavis

in** A Discourse Concerning Algebra**

January 2003; p ublished online September 2007 .

Chapter. Subjects: History of Mathematics. 10935 words.

William Oughtred (1573-1660) was renowned throughout his life as a teacher of mathematics and especially, in his later years, for his *Clavis mathematicae*, his textbook on arithmetic and...

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## Arrival in Europe

in** Enlightening Symbols**

December 2016; p ublished online January 2018 .

Chapter. Subjects: History of Mathematics. 2787 words.

This chapter examines how our current number system reached Europe. There is a dispute over whether or not the person most responsible for introducing Hindu-Arabic numerals to Europe was...