Solving the Three Ancient Problems using the Graef Curves (ePub)
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The Three Ancient Problems (trisecting the angle, squaring the circle, duplicating the cube) have challenged mathematicians for over 2000 years. It's been proven that it's impossible to solve these problems using compass and straightedge alone, so mathematicians were challenged to create a curve or family of curves to solve all three. Until Edward V. Graef invented his Graef curves, no mathematician had accomplished this feat--not Archimedes, not Nicomedes, not Hippias. His solution has been verified by top mathematicians, and published in prestigious math publications.
"Mr. Graef's discovery of the method of trisecting the angle is indeed commendable, his discovery of the method of squaring the circle is remarkable, and his finding of his method of duplicating the cube is truly almost unbelievable.... Mr. Graef accomplished the feat of solving all three problems using methods of geometry, using the same family of curves (not constructible with compass and straightedge alone) for all three." Dr. Vincent C. Harris, Professor Emeritus, San Diego State College (now University).
"Graef's method [solve all three problems with one class of curves alone] passed the scrutiny of the most rigorous analysis." Professor Henry Gould, West Virginia University
The Graef curves were proven in analytic geometry in an article coauthored by Edward V. Graef and Dr. Vincent C. Harris: "On the Solutions of Three Ancient Problems," published in Mathematics Magazine. This published Mathematics Magazine article was subsequently favorably reviewed in the German journal "Zentralblatt."
Another paper was coauthored by Edward V. Graef and Dr. Vincent C. Harris: "A Method of Duplicating the Cube," which was published in Mathematics Magazine.
Dear Abby featured the Graef curves in an answer to who solved the Three Ancient Problems.
1911 - 1989
Edward V. Graef was a gifted mathematician though he had no formal training in math. He had a M.A. in Social Administration from Ohio State University and a B.S. in History and Education from City College of New York. By the time he retired, he was Executive Director of the Health Research and Services Foundation in Pittsburgh (part of the United Fund (United Way)), and was responsible for creating the Health-O-Rama, which provided free health screening.
Edward served as an Army infantry captain in the Philippines during WWII, and was awarded a Bronze Star. He first demonstrated his mathematical abilities while in the service. He devised a method of firing mortar when the sight is lost or broken, and received a Legion of Merit commendation for the effort.
While in the service, Edward married Eleanor Marshall, an American Red Cross volunteer and the daughter of a former mayor of Columbus, Ohio. They had four children: Ed, John, Howard, and Marsha. It was while helping his children with geometry homework that his interest in the Three Ancient Problems began.
Edward was also an accomplished writer. He took the daily letters he wrote to his wife during WWII, and compiled them into a memoir. Entitled "War Letters: Eleanor, My Darling--a Memoir of WWII", it is available as an eBook.
- Autor: Edward V. Graef
- 2011, 23 Seiten, Englisch
- Verlag: Distributed via Smashwords
- ISBN-10: 1465852611
- ISBN-13: 9781465852618
- Erscheinungsdatum: 25.09.2011
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- Größe: 1.25 MB
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