Wednesday, April 19, 2017
Nice Egg on a Budget
Nice Egg on a Budget
Last week I invited all readers to submit their fun math stories and puzzles and already received two interesting pointers. One is from Jerome - one of our best puzzle solvers. Jerome lives in Alberta, Canada, where enemies are rare, politics is uneventful, weather is peaceful, and people can devote a lot of time to things that really matter, like food. They grow it, they make it, they eat it and apparently build monuments to the food they like.
Jerome sent me links to the Sausage Monument in Mundare:
Pyrogy (on a fork) Monument in Glendon:
Jerome sent me links to the Sausage Monument in Mundare:
Pyrogy (on a fork) Monument in Glendon:
And a Ukranian Easter Egg Monument in Vegreville:
The Easter Egg is called Pysanka and it commemorates the Ukranian heritage of the large part of Vegreville population. It measures 25.7 feet long and stands 31 feet high. Complicated geometry of the egg shape made the design of the Pysanka a highly complex project. Professor Ronald Resch, a computer scientist at the University of Utah, agreed to take on the design work.
So, how do you build a giant replica of a chicken egg accurately, decoratively, and inexpensively in 1980th?
According to one of the Reschs students, they chose not to use the usual method of splitting the egg surface into latitudinal and longitudinal lines as this would produce a very large number of un-indentical parts that would drive project costs up. Instead, they decided to approximate the egg surface with small equilateral triangular tiles made of aluminium. Professor Resch already worked on similar but much simpler curved surfaces for some dome architectural projects. He started with folding paper experiments and noted interesting symmetrical patterns that un-folded paper creates. Over the period of a year together with his students Resch designed a special computer program that can figure out the numerous folds that can lead to the egg shape. You can see all the math details in this old paper by one of Reschs students, James Blinn, that became one of the star computer scientists. They then produced the egg on the Universitys flat-bed plotter machine, out of aluminium, replacing the plotter pen with the milling tool. Each side of the equilateral triangle was made to be 1 foot long. The triangles were anodized in three colors and bolted together.
The Pysanka ended up as an immense jigsaw puzzle containing 524 star patterns, 1,108 equilateral triangles, 3,512 visible facets, 6,978 nuts and bolts, and 177 internal struts. This believed to be the first case of laying a computer generated egg.
So, how do you build a giant replica of a chicken egg accurately, decoratively, and inexpensively in 1980th?
According to one of the Reschs students, they chose not to use the usual method of splitting the egg surface into latitudinal and longitudinal lines as this would produce a very large number of un-indentical parts that would drive project costs up. Instead, they decided to approximate the egg surface with small equilateral triangular tiles made of aluminium. Professor Resch already worked on similar but much simpler curved surfaces for some dome architectural projects. He started with folding paper experiments and noted interesting symmetrical patterns that un-folded paper creates. Over the period of a year together with his students Resch designed a special computer program that can figure out the numerous folds that can lead to the egg shape. You can see all the math details in this old paper by one of Reschs students, James Blinn, that became one of the star computer scientists. They then produced the egg on the Universitys flat-bed plotter machine, out of aluminium, replacing the plotter pen with the milling tool. Each side of the equilateral triangle was made to be 1 foot long. The triangles were anodized in three colors and bolted together.
Available link for download
