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Ptolemy's Almagest
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Diophantus's Arithmetica
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History of Math #2
The Math Book (years 0 -1400)
| Term | Definition |
|---|---|
| Ptolemy's Almagest | 150. Ptolemy a mathematician and astronomer. Wrote Almagest with everything known about space. Trig table for sine values from 0 to 90, also law of sines, compound angle and half-angle identities |
| Diophantus's Arithmetica | 250. Greek mathematician the father of algebra. Treatment of fractions as numbers, like integer solutions to equations. |
| Pappus's Hexagon Theorem | 340. Farmer planting 9 trees in 10 rows. Put 3 in a row, 3 in a row, draw lines, hexagon reveals 3rd line. Then adjust. Important because a theorem was established free from measurements. First projective geometry. |
| Bakhshali Manuscript | 350. Found in India in a stone enclosure in 1881. Had techniques for arithmetic, algebra, geometry, square roots, and also zero, negatives, and unknowns. First Indian mathematics without religion. |
| Death of Hypatia | 415. Female Greek mathematician, Christians seized her, scraped her skin off, and cut her to pieces. Marked end of Greek progress in mathematics. |
| Zero | 650. Ancient Babylonians had no symbol...used a space (confusing). India...it was common...and spread to Arabs, Europeans and the Chinese. Mayans also but didn't spread from there. |
| Alcuin's Propositiones ad Acuendos Juvenes | 800. Alcuinus a scholar from England. His book contributed to the learning of the "Number Pope" in France who redid the floor of a cathedral as an abacus and adopted Arabic numbers in place of Roman Numerals. The book has puzzles including river crossings |
| Al-Khwarizmi's Algebra | 830. Father of Algebra. From Persia/Baghdad. Al-jabr an operation to add the same quantity to both sides of an equation, book intended to be practical with linear & quadratic equations |
| Borrowmean Rings | 834- Three interlocking rings (Italian family name crest). Cut one and they all fall apart. (Cannot really make) |
| Ganita Sara Samgraha | 850. Indian book. Problem about a girl with lots of pearls on necklace. Square root of a negative doesn't exist, ellipses, etc. |
| Thabit Formula for Amicable Numbers | 850. Arab. Formula for amicable numbers. Amicable numbers are two numbers whose proper factors sum to the other number. (220 & 284) |
| Chapters in Indian Mathematics | 953. Book written by Arab Al-Uqlidisi. Translated Euclid's works. Used decimals for first time, legacy is paper-and-pen math (instead of sand) |
| Omar Khayyan's Treatise | 1070. Persian known for poetry. Also derived methods for solving cubic equations with geometric solutions by means of intersecting conic sections. Also found how to obtain (a+b)^n like Pascal's Triangle |
| Al-Samawal's The Dazzling | 1150. Jewish man in Baghdad later converted to Islam. Arithmetization of algebra, x to the power of zero = 1 and found a formula for the sum of squares. |
| Abacus | 1200. Used in ancient times. Modern abacus with beads on wires in China. Predecessor to computer. Experienced users can quicky multiply, divide and find square roots. |
| Fibonacci's Liber Abaci | 1202. Italian. Book introduced Hindu-Arabic numerals to Western Europe. And then of course the Fibonacci Sequence. |
| Wheat on a Chessboard | 1256. Arab scholar Ibn Khallikan first author to discuss this story which is important because it illustrates geometric growth. |
| Harmonic Series Diverges | 1350. A divergent series approaches infinity (1+2+3...). The harmonic series 1 + 1/2 + 1/3 + 1/4 also approaches infinity but much more slowly. |
Created by:
kzmom314
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