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Pythagorean
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151	The Blakers Mathematics Contest 2008 Solutions 1. An even sum Let n ≥ 2 and let a1 , a2 , . . . , an be integers. Prove that \|a1 − a2 \| + \|a2 − a3 \| + · · · + \|an − a1 \| is even. Solution (Y. Choong, 1st year, Add to Reading List Source URL: www.maths.uwa.edu.au Language: English - Date: 2009-05-04 03:36:44 Elementary mathematics Trigonometric functions Inverse trigonometric functions Sine Pythagorean trigonometric identity Trigonometry Mathematics Mathematical analysis
152	Pythagoras and the story behind the Croton Crown Archaeological survey indicates the Dark Ages of Greece extended from the eleventh to the eighth Century BCE. Bizarre reasons including an increase in population were attr Add to Reading List Source URL: www.avesta.org Language: English - Date: 2011-12-29 21:32:33 Philosophy of mathematics Triangles Ancient Greek mathematicians Esotericists Mystics Pythagoras Pythagorean theorem Pythagoreanism Crotone Mathematics Geometry Esotericism
153	Developing and Composing With Scales based on Recurrent Sequences Warren Burt freelance composer PO Box 2154, St. Kilda West, VIC 3182 email: [removed] Add to Reading List Source URL: www.warrenburt.com Language: English Intervals Greek music Pythagorean philosophy Pythagorean tuning Just intonation Semitone Perfect fifth Cent Rothenberg propriety Pitch Musical tuning Measurement
154	Catalog of Scales used in 18 New Fuguing Tunes for Henry Cowell - Warren Burt 2005 A listing of all[removed]note Euler Fokker Genera scales possible with factors 3 5 and 7 arranged in the order that produces minimal change Add to Reading List Source URL: www.warrenburt.com Language: English Intervals Pythagorean interval Comma Semitone Septimal comma Diesis Tritone Harmonic Perfect fifth Pitch Musical tuning Sound
155	ADFS::HardDisc4.$.UKMT.JOS.imok.booklets.2015.PoScript Add to Reading List Source URL: www.ukmt.org.uk Language: English - Date: 2015-03-31 05:46:20 Euclidean geometry Triangle Right triangle Pythagorean theorem Equilateral triangle Mathematical fallacy Geometry Triangles Triangle geometry
156	In Geometric Science of Information, 2013, Paris. Law of Cosines and Shannon-Pythagorean Theorem for Quantum Information? Roman V. Belavkin1 School of Engineering and Information Sciences Add to Reading List Source URL: www.eis.mdx.ac.uk Language: English - Date: 2013-05-23 12:46:39 Mathematics Statistical theory Kullback–Leibler divergence Logarithm Information geometry Divergence Pythagorean theorem Entropy Conditional mutual information Statistics Geometry Information theory
157	Sound: A Basis for Universal Structure in Ancient and Modern Cosmology1 Jung Hee Choi Since all sound may be measured and expressed in number, and the relationships of numbers can be precisely translated into intervals t Add to Reading List Source URL: drawastraightlineandfollowit.com Language: English - Date: 2014-06-23 17:19:18 Mathematics of music Musical tuning Pythagorean philosophy Acoustics Ernest G. McClain Pythagorean comma Pythagoreanism Music and mathematics Pythagoras Music Pitch Intervals
158	Microsoft Word - Junior Maths.doc Add to Reading List Source URL: www.completeschool.com.au Language: English - Date: 2010-03-06 03:56:23 Mathematics Right triangle Trigonometric functions Hypotenuse Sine Pythagorean theorem Generalized trigonometry Pythagorean trigonometric identity Law of tangents Geometry Trigonometry Triangles
159	Microsoft Word - 3550455B.rtf Add to Reading List Source URL: www.funmaths.com Language: English - Date: 2006-01-11 21:11:20 Triangle geometry Elementary geometry Angle Triangle Hypotenuse Right angle Adjacent Right triangle Pythagorean theorem Geometry Triangles Trigonometry
160	Catalog of scales made with Additive Sequences for “The MOSsy Slopes of Mt. Meru. Warren Burt[removed]These scales embody the following additive sequence rules Sequence Rule An = An-2 + An-1 Bn = Bn-3 + Bn-1 Add to Reading List Source URL: www.warrenburt.com Language: English Intervals Greek music Pythagorean philosophy Pythagorean tuning Cent Musical scales Musical tuning Pitch Measurement

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