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# Pythagoras and Geometry

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Geometry Workbook highlighting applications and history of geometry and mathematics

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### Pythagoras and Geometry

1. 1. Book Title : Geometry Mathsfill Author : C.J. Davis Level : GCSE ISBN 9780956014672 GCSE Maths Workbook Applications of Geometry History of Geometry
2. 2. Discoveries of famous mathematicians Read about : Euclid ( 365 – 265 BC ) Democritus ( 460 BC – 370 BC )
3. 3. Some of the major contributors in the development of geometry. Archimedes c. 290 BC also : Pythagoras c. 570 BC
4. 4. exactly two-thirds that of the cylinder surrounding it. the volume and surface area of a sphere is proved that . . . Archimedes
5. 5. Archimedes was the first person to give the exact expression for the volume of a sphere . . . 4 3  r 3 V =
6. 6. The medal carries a portrait of Archimedes. The inscription around the medal is a quote in Latin attributed to Archimedes : “ Rise above oneself and grasp the world . ” The Field’s medal is awarded to mathematicians of outstanding achievement . The Field’s Medal
7. 7. Volume of pyramid, V =  x area of base x height . . . worked on the general formula for the volume of a pyramid : Democritus
8. 8. For a right-angled triangle the square on the hypotenuse is equal to the sum of the squares on the other two sides. is best known for his Pythagorean theorem which states : Pythagoras
9. 9. Old Babylonian &quot;hand tablet&quot; illustrating Pythagoras' Theorem and an approximation of the square root of two. The Babylonians understood this rule 1 000 years earlier, but Pythagoras proved it.
10. 10. . . . created the earliest systems . of weights and measures ? WHO . . . ? . . . devised the Metric system ?
11. 11. The Metric system was created by the French Academy of Science in 1793. A team of mathematicians and scientists were involved in its creation. Antoine Lavoisier ( 1743 -1794 ) This included the mathematician Joseph Lagrange and the chemist Antoine Lavoisier.
12. 12. GCSE Maths Workbook Applications of Geometry History of Geometry
13. 13. WHAT . . . ? . . . is the numerical value . of pi ?
14. 14. HOW . . . ? is trigonometry used to calculate the height of a tree ?
15. 16. WHAT . . . ? . . . is the Cornrow Curves Software ? . . . are the four geometric concepts used to create cornrow hairstyles ? www.rpi.edu/~eglash/eglash.htm
16. 17. The Cornrow Curves software was created by Prof. Ron Eglash and allows you use geometrical knowledge from cornrow hairstyles to create your own simulated cornrow designs on the computer. www.rpi.edu/~eglash/eglash.htm
17. 18. What are Fractals ? Each leaf of this fern is in fact a smaller version of the entire fern. The whole fern is simply made up of reduced versions of itself.  Fractals are images that exhibit something called self-similarity .  e.g. something that is made up of a reduced version of itself.
18. 19. . . . is the link between fractals , African art, architecture and designs ? WHAT . . . ?
19. 20. The brachistochrone curve is an inverted cycloid. The cycloid occurs as the curve generated by a point on a rolling circle. HOW . . . ? . . . is a cycloid generated ?
20. 21. Is the shortest path always the quickest ? WHICH . . . ? Set up a straight line path and a brachistochrone and see ! . . . path is the quickest route to the bottom ?
21. 22.   Linear Descent vs. the Brachistochrone When two balls are dropped from the top of the straight ramp and the the bottom first, even though the path it travels is longer. brachistochrone top of the brachistochrone, the ball on the brachistochrone reaches
22. 23. GCSE Maths Workbook Applications of Geometry History of Geometry
23. 24. - Time saving, write-on format. - Clearly structured, easy to follow layout. What are students saying about Geometry Mathsfill ?
24. 25. A skateboard ramp has a height of 1.05 m and a base of 2.24 m. Calculate the length of the ramp, 2.24 m 1.05 m m …………………………………………… .………..….. ……………………………………… .… …………… m …………………………………………… .………..…..
25. 26. …………………………………………… .……………………...….. ………………………………………………… .… ………….…… km …………………………………………… .………………….…..….. From take-off an aeroplane climbs at an angle 12. of 18  . When the aeroplane has flown 15 km, what vertical height has it reached ?
26. 27. Foyles Bookshop Charing Cross Road London WC1 England Available ( online ) at : www.Foyles.co.uk Available ( in-store ) at : ISBN 9780956014672 Geometry Mathsfill ( A5 ) Notepad format Author: C.J. Davis Publisher : Bookfill Price £ 11.99
27. 28. ALSO available : log onto www.bookfill.co.uk for more details ISBN 9780956014603 ( A5 ) Notepad format Algebra Mathsfill Price £ 11.99 Author: C.J. Davis Publisher : Bookfill