Did Mesopotamian Scribes Have Algebra? (And How Can We Recognize 'Rhetorical' and 'Syncopated' Algebra?) Yes, Babylonian scribes had algebra, but not the kind we use today. They had rhetorical algebra , which means everything was written out in words, with no symbols for unknowns or operations. A problem might say: “I have subtracted the side of the square from the area, and the result is 14,30.” We would write that as x 2 − x = 870 x^2 − x = 870 . The scribes solved quadratic equations using step-by-step verbal recipes: halve the coefficient, square it, add, take the square root. The method was general, but the generality lived in the procedure, not in a formula. Later, Diophantus used syncopated algebra, a middle stage with abbreviations for common quantities and operations. The Babylonians stayed rhetorical. This raises big questions: How do you state a general principle without symbols? By repeating the same procedure with different numbers and d...
Posts
- Get link
- X
- Other Apps
Here is my Babylonian-style base-60 multiplication table for 45. I use commas to separate sexagesimal places. So 22,30 means 22 + 30/60, and 5,37,30 means 5 + 37/60 + 30/3600. Sexagesimal Factorization: Base-60 Factor Pairs for 45 I found these five pairs that multiply to 45 (not using 1): - 3 X 15 = 45 - 4 X 11,15 = 45 Check: 11,15 = 11 + 15/60 = 11.25, and 4 X 11.25 = 45 - 5 X 9 = 45 - 6 X 7,30 = 45 Check: 7,30 = 7 + 30/60 = 7.5, and 6 X 7.5 = 45 - 8 X 5,37,30 = 45 Check: 5,37,30 = 5 + 37/60 + 30/3600 = 5.625, and 8 X 5.625 = 45 So, including the example 2 X 22,30 = 45, there are at least six pairs that work. Three of my new pairs include base-60 fractions. This was a good way to practice thinking in base 60 and to see how fractions work in a sexagesimal place-value system.
- Get link
- X
- Other Apps
Why Teach Math History? My First Response Before reading Tzanakis and Arcavi’s survey, I thought of math history as mostly enrichment. I imagined names, dates, and fun facts, maybe a short story about Pythagoras or a poster of ancient numerals. I did not see it as central to actually teaching mathematics. I also worried that adding history would take time away from an already packed curriculum, and I was not sure how I would assess it. If I used history at all, I assumed it would be as a hook or a break from the “real” math, not as a serious teaching approach. Several things in the article made me stop and think. First, the authors honestly list the common objections, history is not math, there is not enough time, resources, or teacher expertise, and assessment is unclear. I appreciated that they did not just cheerlead for history. Second, I was surprised by the idea of a “genetic” or history-inspired approach: using the historical development of an idea to design a sequence of p...