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Four planes from the axial pencil on P1 P2. A pencil of planes, is the set of planes through a given straight line in three-space, called the axis of the pencil. The pencil is sometimes referred to as a axial-pencil [7] or fan of planes or a sheaf of planes. [8]
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First Lessons drew inspiration from Fröbel's gifts in setting exercises based on paper-folding, and from the book Elementary Geometry: Congruent Figures by Olaus Henrici in using a definition of geometric congruence based on matching shapes to each other and well-suited for folding-based geometry.
Geometric Origami is a book on the mathematics of paper folding, focusing on the ability to simulate and extend classical straightedge and compass constructions using origami. It was written by Austrian mathematician Robert Geretschläger [ de ] and published by Arbelos Publishing (Shipley, UK) in 2008.
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Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician who works in the field of geometry is called a geometer. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, [a] which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental ...
Book I is titled Problems Which Can Be Constructed by Means of Circles and Straight Lines Only. In this book he introduces algebraic notation that is still in use today. The letters at the end of the alphabet, viz., x , y , z , etc. are to denote unknown variables, while those at the start of the alphabet, a , b , c , etc. denote constants.
The main topics of the book are the Platonic solids (regular convex polyhedra), related polyhedra, and their higher-dimensional generalizations. [1] [2] It has 14 chapters, along with multiple appendices, [3] providing a more complete treatment of the subject than any earlier work, and incorporating material from 18 of Coxeter's own previous papers. [1]
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