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History of Math #3
The Math Book (years 1400-1700)
| Term | Definition |
|---|---|
| Law of Cosines | 1427- C2 = a2 + b2 - 2ab(cos C). Used for finding missing sides/angles in a triangle. Becomes the Pythagorean Theorem when C = 90 and cos = 0. Discovered by Persian al-Kashi and Frenchman Francois Viete |
| Treviso Arithmetic | 1478- First math book, Italian, used lots of word problems about merchants, interest, cheating, etc. Had Hindu-Arabic numbers and algorithms. |
| Discovery of Series Formula for Pi | 1500- Pi/4 = 1 - 1/3 + 1/5 - 1/7 + 1/9....Discovered independently by several mathematicians. Similar to arctan series |
| Golden Ratio | 1509- Draw a line. Divide in two so the ratio of the whole: longer part = the ratio of the longer part: the shorter part. 1.61803. A golden rectangle can be split into a golden rectangle and a square, making a spiral.. center called "Eye of God" |
| Polygraphiae Libri Sex | 1518- First printed book about codes (Six Books of Polygraphy) written by German abbot Johannes Trithemius. Two columns of words and letters...each word represents a letter. |
| Loxodrome | 1537- Pedro Nunes of Portugal. This is a line on a globe so that ships can travel on the same heading. Appears as a straight line on a Mercator Projection. Pedro Nunes was a Jew forced to convert to Catholicism as a child during the Inquisition. |
| Cardan's Ars Magna | 1545- Italian algebra book. Very repetitive with similar problems. Did have solutions to different types of cubic and quartic equations. Important part was exploration of imaginary numbers. Thrown in jail for casting the horoscope of Jesus. |
| Sumario Compendioso | 1556- First math book published in the New World- Mexico. Written by Juan Diez, companion of Cortex. Mostly for people buying god & silver...lots of tables so they didn't have to do math. |
| Mercator Projection | 1569- By Flemish man Mercator. Straight lines are loxodromes, lines of constant compass heading. Areas too big at the poles. |
| Imaginary Numbers | 1572- Italian engineer Rafael Bombelli who was famous for draining swamps, notated it. May mathematicians hesitant, including Descartes who gave it the dubious moniker imaginary. |
| Kepler Conjecture | 1611- This conjecture tells how many spheres can be packed into a box. You have to create a hexagon arrangement at the bottom and then put the spheres into the indentations. Density about 74% |
| Logarithms | 1614- Scottish mathematician John Napier is the inventor. Makes difficult problems simpler. There were tables used. Today base 10 used in pH scale, acoustics and Richter scale. |
| Slide Rule | 1621- Invented by Englishman William Oughtred...whose student STOLE the idea and published it. Slide rules used until the invention of the calculator |
| Fermat's Spiral | 1636- Fermat a French lawyer, also math...Fermat spiral is a parabolic spiral in polar. Studied the relationship of the area enclosed by the arm and the x-axis. Used for plant seed heads. |
| Fermat's Last Theorem | 1637- Fermat a French lawyer. Co-founder of probability thero (with Pascal). Co-founder of anal. geom (with Descartes.) FLT says x^n + y^n = z^n has no nonzero integer solutions if n>2. Finally proven in 1994 |
| Descartes' La Geometrie | 1637- Book showed how geometric shapes can be analyzed with algebra by putting them on a graph (although he didn't use any coordinate system) |
| Cardioid | 1637- A heart shaped figure drawn with lines. Make it by taking a fixed point on a circle and tracking it as it rolls around another circle of the same radius. |
| Logarithmic Spiral | 1638- spirals of shells, mammal horns, plant seeds, galaxies, first discussed by Descartes and later Bernoulli, r = ke^aθ, spiral form can allow for the compaction of a relatively long length |
| Torricelli's Trumpet | 1641- Take f(x) = 1/x and revolve it around the x-axis and you get a trumpet with seemingly finite volume and infinite surface area. Also called Gabriel's Horn. |
| Pascal's Triangle | 1654- Probability Theory and the expansion of (x+y)^n, SO MANY patterns, when evens are replaced by a dot and odds by a space, you get a fractal |
| Length of Neile's Semicubical Parabola | 1657- British man William Neile became the first person to rectify, or find the arc length of, a nontrivial algebraic curve. It was x^3 = ay^2 OR y = ax^(3/2) |
| Viviani's Theorem | 1659- In an equilateral triangle, place a point anywhere and draw perpendicular lines to the sides. The sum of those lines will the height. (Kids do this problem with a surfer building a hut on a triangle island). Extrapolated to other polygons. |
| Discovery of Calculus | 1665- English Isaac Newton & German Gottfried Wilhelm Leibniz. Both studied tangents, rates of change, minima, maxima, differentials, and integrals. |
| Newton's Method | 1669- Method for solving equations of the form f(x) = 0. Simply guess, then find that tangent line and its x-intercept and repeat. |
| Tautochrone Problem | 1673- Looking for a ramp that no matter where you place an object it will slide down to the bottom in the same amount of time. Dutch mathematician Christiaaan Huygens figured it out...it's part of a circle. |
| Astroid | 1674- This curve is made by running a circle around the inside of another circle (spirograph) and is made by a point on the edge. Many mathematicians studied it. |
| L'Hopital's Analysis of the Infinitely Small | 1696- French mathematician L'Hopital published first calculus book.. Hired Bernoulli to teach him calculus and also paid him to tell him discoveries which he included in his book. |
Created by:
kzmom314
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