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Construction of geometric figures & numbers

Construction of geometric figures & numbers. Presenters: Harris, Joanne Poletti, Mitsuko. History. Thales (600 BC). Hippocrates (440 BC). Euclid (300 BC). Archimedes (220 BC). History. Egyptian (1800 BC). Babylonian (3000 BC). Chinese (400BC). Indian (900 BC).

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Construction of geometric figures & numbers

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  1. Construction of geometric figures & numbers Presenters: Harris, Joanne Poletti, Mitsuko

  2. History • Thales (600 BC) • Hippocrates (440 BC) • Euclid (300 BC) • Archimedes (220 BC)

  3. History Egyptian (1800 BC) Babylonian (3000 BC) Chinese (400BC) Indian (900 BC)

  4. How to make Geometric figures • Sketching/Drawing By free hand Or any tools • Compass-and-straight-edge Construction

  5. Warm up Construct the following using pencil, compass and straight edge only. Do not fold the paper! • 3/4 unit ( 1 unit is given below) • Bisect a given angle

  6. Share with others • 3/4 unit Do you see different ways of construction? • Bisect an angle

  7. Rules of Construction • Euclid’s • construction rule • Construction rules that are well accepted by modern society

  8. What are the advantages of applying Euclid’s Rule? Open Discussion • When we use less tools to build geometric figures, we apply more geometric properties. • The compass method is usually more precise as it does not rely on the correct measurement of angles or lengths.

  9. Can we construct the following ? • Equilateral Triangle • Isosceles Triangle

  10. Find the center of a circle If it is on a piece of paper…? What if it is a steel ring…? What if it is a steel disk…?

  11. Inscribed Regular Polygons An inscribed equilateral hexagon

  12. Inscribed Regular Polygons An inscribed equilateral triangle

  13. Inscribed Regular Polygons An inscribed Square

  14. Inscribed Regular n-gons Inscribed regular dodecagon

  15. Over Lapping The minor Arc CK= 1/3 of the circumference The minor arc CF=1/4 of the Circumference The minor arc FK = 1/3 - 1/4 = 1/12 of the circumference

  16. Inscribed Pentagon and Phi is called a golden triangle

  17. phi AG=X DG=X-1 AB=1 rectangle ABFG  rectangle GDCF

  18. Can we find a geometric length of any number using the unit of 1 ? 2 units ¾ unit …? 0.4 5/4 1/3

  19. Construction of Fractions n=a/b

  20. Irrational Numbers

  21. Square root of any integer “n” Beautiful? Tedious?

  22. What if n is a large number? Applying geometric mean

  23. What about pi? e?

  24. Beauty of Geometric Construction

  25. Modern architectures and arts

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