Deezynar, he is showing how to find root 2 and root 3 before the video ends. In two more similar steps he would have shown how to physically show root 5. Then that length added to 'one' and then bisected would be phi, the golden section, 1.618......it's just a proportion. Hope that helps.
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Every rectangle has 4 line & 4 corner points. If you connect those points they reveal more lines and points. This process creates a grid which also gives you 5 to 7 line directions. Like a master painter who limits his palette so will a master draftsmen limit the his line directions. He will determent those 5 to 7 directions by the rectangle they're composing in.
For anyone interested in how the golden ratio is derived geometrically, look up Euclid's: The Elements Book 2, Proposition 11. It'll show how you can derive this with just a simple straight edge and compass.
Yes. they are 2 different rectangles. Golden Section: 1. Draw a Square. 2. Draw a line from the top-right corner to the MIDDLE of the bottom line. 3. Redraw the bottom line so it's as long as the diagonal you just drew. Root Two: 1. Draw a Square. 2. Draw a line from the top-right corner to the bottom-LEFT corner. 3. Redraw the bottom line so it's as long as the diagonal you just drew.
The only method simpler I've found was in Adobe Illustrator ( and like software ). But doing it by hand - I'd love to see a simpler way, How are you doing it?
I'm not sure I understand what he meant when he said intervals gave the Egyptians a golden section triangle. Since the golden section is irrational, how could anyone derive it from from a rope knotted at rational intervals? Anyone have insight about this?
I can't see any good reason to relate the golden ratio to art. The reasons given are that a whole heep of people did before due to their beliefs and that it exists in many forms of nature, which really aren't reason at all, especially as it's not evident unless measured. Most importantly I believe the same aesthetically pleasing conclusions found can be made in much quicker more efficient ways as it's certainly not the only form that governs and determines our spatial tastes we find pleasing. Regardless I'm very interested, and shall investigate the aesthetic reasons for employing the golden ration..
