Reading Questions #8

Reading Questions #8 - 12 volumes and areas 13 the golden...

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Read pages 139-161 and submit your answers to these questions before 7 am on Monday, 10/22: 1. What is the relationship between the golden ratio and the Fibonacci numbers? F(n+1)/F(n) As the nth number in a Fibonacci sequence gets larger, the closer the sequence comes to the Golden Ratio of (1+√5)/2 2. Give a very brief description of each of the 13 books of Euclid's Elements. 1. all about basic Geometry. 2. shows equations having to do with geometric algebra including the golden ration. 3. how to find circles and the angles of the circle, all 360 of them. 4. polygons and their points 5. ratios, irrational numbers. 6. similar geometric shapes and proportions. number theory {7. Primes, GCDs, common multiples 8. squares and cubes of numbers 9. infinite number of primes, perfect numbers.} number theory 10. measurements. 11. planes and polygons and lines on them.
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Unformatted text preview: 12. volumes and areas. 13. the golden ratio with polygons and 3 dimensional shapes whose faces are congruent. 3. What is a regular solid? What are the 5 regular solids? a regular solid is a "three- dimensional figure having planar faces, with each face a regular polygon, all faces congruent and all angles between pairs of adjacent faces the same."(Devlin 148) The five regular solids are the: Cube, Tetrahedron, Octahedron, Dodecahedron, and Icosahedron. 4. Why is the standard xy-plane called the Cartesian coordinate system? Why was this such a crucial innovation? It was invented by Descartes whose name in Latin was Cartesius and therefore the grid was named Cartesian after Descartes. the system was most important because it enabled mathematicians to use algebra techniques to play with geometry...
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