1 / 25

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).

noleta
Download Presentation

Construction of geometric figures & numbers

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related