tag:blogger.com,1999:blog-2207789741693789296.post6552273465217892791..comments2022-05-02T01:44:44.795-04:00Comments on Cool Math Stuff: Fibonacci Day: Some Additional Fibonacci FunEthan Brownhttp://www.blogger.com/profile/09611695185154134251noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-2207789741693789296.post-2256578075618478502012-06-04T00:21:17.546-04:002012-06-04T00:21:17.546-04:00If you like Golden Rectangles, you will love ISO 2...If you like Golden Rectangles, you will love ISO 216:<br /><br />http://www.cl.cam.ac.uk/~mgk25/iso-paper.html<br />http://wikipedia.org/wiki/ISO_216<br /><br />This leads to grammage:<br /><br />http://wikipedia.org/wiki/paper_density<br /><br />Since we get into measures and standards, we might as well get into Planck-Units:<br /><br />http://wikipedia.org/wiki/Planck_UnitsWalabiohttps://www.blogger.com/profile/17344805981006822411noreply@blogger.comtag:blogger.com,1999:blog-2207789741693789296.post-51262852715699790552012-06-03T23:49:34.386-04:002012-06-03T23:49:34.386-04:00The video mentioned the Egyptian Pyramids:
0thly,...The video mentioned the Egyptian Pyramids:<br /><br />0thly, I do not get the fascination with huge piles of stone. the usable volume of a pyramid is less than < .1%. The nonstructural volume of modern skyscrapers is about ~90%. After subtracting utility-space (airducts, crawlspaces, et cetera) is still about ~ 80%. The enclosed volume of geodesic domes* and monolithic domes*(which honestly, because of extremely high ceilings, may be hard to fully utilize from the ground all of the way to the ceiling) is greater than > 99.9%.<br /><br />* http://wikipedia.org/wiki/geodesic_dome<br />* http://wikipedia.org/wiki/monolithic_dome<br /><br />As for τ/4 or ϕ appearing in the Egyptian Pyramids, that is an accident:<br /><br />The Egyptian Cubit, believed to be the length of the forearm of an early Egyptian Pharaoh, was the unit the Egyptians used to measure length. The Egyptians had only a vague idea about τ.<br /><br />One defines the standard Egyptian Pyramid has a base x rolls of a wheel with a diameter of 1 Egyptian Cubit and 2x number of rolls in cubits high. Initially, the ration of base to height was τ/4.<br /><br />Because of erosion, the ratio of base to height has often closer or even gone through ϕ. The Egyptian Pyramids erode faster at the top than the base because the Egyptians built them over > 4,000 BBF (Before Benjamin Franklin):<br /><br />Benjamin Franklin invented the lighting rob along with bifocals, the cast iron stove, et cetera. Lightning strikes the tops of the Egyptian Pyramids. Since stone is a poor conductor, much of the energy becomes heat. Sometimes the stone explodes from the heat. Thus, the Egyptian Pyramids erode faster from the top.Walabiohttps://www.blogger.com/profile/17344805981006822411noreply@blogger.com