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Pythagorean Triangle Properties and Attributes Samples (Enlarged), As Independently Discovered by Colin Gardner, Physicist
Colin Gardner
其他書名
Pythagorean Triples are Everwhere, and Have an Application in Nearly Every Math Lesson(6th Grade Thru College
出版Colin Gardner, 2004-04
主題Juvenile Nonfiction / Mathematics / General
ISBN09720348549780972034852
URLhttp://books.google.com.hk/books?id=xRv5PAAACAAJ&hl=&source=gbs_api
註釋This ISBN unequivocally shows Pythagorean triples comes from parabola equations, with examples for x-axis and y-axis. Three algebraic equations provide triples for every triangle leg > 2, with common sides 2,3-50+. Two dozen different equations provide 20+ identical answers for PN1 + QN2 + RN3 with 7 examples meeting a*a + b*b = c*c as INTEGERS. Students can create quadratic equations for Pythagorean triangles using 4 new parameters related to P,Q and R. Ellipses have integer triples coincident with their curves. Use PARABOLIC equations to modify integers or equations on right triangle sides where what is SEEN on its legs can then be ADDED to obtain its hypotenuse value. Normal looking algebraic equations provides one triple and also can DEFINE a triangle having a missing side when either P,Q or R is zero. Develop two non-Pythagorean triangles, which when adding and subtracting these angles in a new triangle, where full triples result. Twelve General Equations provide triple solutions ,some algebraic, to cubic, tangent or cotangent equations. Many General Equations plus 40 more trig equations provide one integer sides for triples. Equations to find shortest lengths of LARGE triples is provided, also puts sides on triangles having only one known angle. Pythagorean ratios, for any two sets of pairs of integers, equivalent to trig identities is provided. Students and teachers are encouraged to evaluate the validity and significance of these equations.