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Golden Ratio / Section

Enrichment PowerPoint Presentation

Golden Ratio / Section


We start the presentation by looking at the original problem as discussed by Euclid in his Elements. The golden proportion phi = 1.618… is then derived. We then move on to look at the aesthetically pleasing Golden Rectangle. The students are then given an opportunity to see if they can correctly choose two golden rectangles from a slide full of rectangles. After this we look at how the golden proportion may have been deliberately used by the ancient Egyptians in the construction of the Great Pyramid at Giza (Cheops). We look at a cross section of the pyramid and examine the mathematics. Much later, the ancient Greeks used the proportion extensively in the construction of the Parthenon in Athens and we see how it fits nicely inside a golden rectangle.
We then discuss the use of the golden proportion throughout renaissance Europe in mathematics, art and architecture. Examples chosen are Galileo’s “Vitruvian Man” and Michelangelo’s “David”. After that we briefly look at modern examples of the use of Golden Rectangles (or at least close approximations to them) and try to encourage students to investigate some themselves.
The “Highly Golden” five starred pentagram, symbol of the Pythagorean Brotherhood, is then constructed and its golden proportion diagonals and golden triangles are looked at.
After this we follow a step by step geometric construction of a Golden Rectangle from a unit square and examine the maths behind the construction. We then look at removing a sequence of squares from a Golden Rectangle and observe the new Golden Rectangle formed each time we repeat this..
The presentation concludes with a very nice animation of a Golden Spiral (approximation) inside the Golden Rectangle.




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