Answer to Question #114171 in Algebra for Lesego

Question

Explain when each of the following algebraic aspect or concepts was developed.State in what part of the world was that aspect or concepts developed.
i. Base ten place value to write numbers
ii Negative coefficient
iii Letters to indicate variables that
iv. Zero
v Equation sign

Answer 1

1. Ancient Egyptian numerals were base 10. They used hieroglyphs for the digits and were not positional. (around 3000 BC) [1]
2. Negative numbers appear for the first time in history in the Nine Chapters on the Mathematical Art (Jiu zhang suan-shu), which in its present form dates from the period of the Han Dynasty (202 BC – AD 220), but may well contain much older material. [2]
3. The use of letters to represent general numbers goes back to Greek antiquity. Aristotle frequently used single capital letters or two letters for the designation of magnitude or number (Cajori vol. 2, page 1). [3]
4. By 1770 BC, the Egyptians had a symbol for zero in accounting texts.
5. According to Lankham, Nachtergaele, and Schilling at University of California-Davis, the first use of the equal sign (=) came in 1557. Robert Recorde, circa 1510 to 1558, was the first to use the symbol in his work, “The Whetstone of Witte.” Recorde, a Welsh physician and mathematician, used two parallel lines to represent equality because he believed they were the most equal things in existence.

[1] https://mathshistory.st-andrews.ac.uk/HistTopics/Egyptian_numerals.html

[2] Struik, page 32–33. "In these matrices we find negative numbers, which appear here for the first time in history."

[3] https://jeff560.tripod.com/variables.html

[4] Joseph, George Gheverghese (2011). The Crest of the Peacock: Non-European Roots of Mathematics (Third Edition). Princeton UP. p. 86. ISBN 978-0-691-13526-7.

[5] https://sciencing.com/history-equality-symbols-math-8143072.html