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A conundrum faced ancient mathematicians. Which number to use for the square root of 2? Ancient Babylonians used the fraction 305470/216000. This was accurate to about six decimal places. Ancient Indians used the fraction 577/408. This fraction is accurate to five decimal places. Today, mathematicians understand that the square root of 2 is irrational, its digits go on forever without repeating. It is calculated using an infinite series. This book lists the first million digits of the square root of 2.

THE Christmas Lectures at the Royal Institution are, by a time-honoured custom, invariably addressed to a "juvenile audience." This term, however, has always been held to be an elastic one, and to include those who are young in spirit as well as those who are young in years. The conditions, therefore, necessarily impose on the Lecturer the duty of treating some subject in such a manner that, whilst not beyond the reach of youthful minds, it may yet possess some elements of interest for those of maturer years. A subject which admits of abundant experimental illustrations is accordingly, on these occasions, a popular one, particularly if it has a bearing upon topics then attracting public attention. The progress of practical invention or discovery often removes at one stroke some fact or principle out of the region of purely scientific investigation, and places it within the purview of the popular mind. A demand then arises for explanations which shall dovetail it on to the ordinary experiences of life. The practical use of æther waves in wireless telegraphy has thus made the subject of waves in general an interesting one. Hence, when permitted the privilege, for a second time, of addressing Christmas audiences in the Royal Institution, the author ventured to indulge the hope that an experimental treatment of the subject of Waves and Ripples in various media would not be wanting in interest. Although such lectures, when reproduced in print, are destitute of the attractions furnished by successful experiments, yet, in response to the wish of many correspondents, they have been committed to writing, in the hope that the explanations given may still be useful to a circle of readers. The author trusts that the attempt to make the operations of visible waves a key to a comprehension of some of the effects produced by waves of an invisible kind may not be altogether without success, and that those who find some of the imperfect expositions in this little book in any degree helpful may thereby be impelled to study the facts more closely from that "open page of Nature" which lies ever unfolded for the instruction of those who have the patience and power to read it aright.J. A. F.UNIVERSITY COLLEGE,LONDON, 1902.

Geometric nets provide many hours of fascinating fun! Each net represents the surface of a unique geometric shape. Some of the shapes were described as much as 2500 years ago.A geometric net is a flat drawing that can be cut and folded into a three dimensional figure. For example, six identical squares can be made into a cube. This is because a cube has six sides, all of which are identical squares. Each of the drawings in this book can be cut and folded into a three dimensional geometric object.This book contains 253 geometric nets, a few of which are:Bielongated Triangular AntiprismConeCubeCuboctahedronCylinderDecagonal AntiprismDecagonal PrismDeltoidal IcositetrahedronDieDisdyakis DodecahedronDodecahedron, RegularElongated Pentagonal BipyramidElongated Pentagonal CupolaElongated Pentagonal PyramidElongated Square BipyramidElongated Square PyramidElongated Triangular AntiprismElongated Triangular BipyramidElongated Triangular CupolaElongated Triangular PyramidFrustum of a Decagon PyramidFrustum of a Quadrilateral PyramidFrustum of a Triangular PyramidGreat DodecahedronGreat Stellated DodecahedronGyroelongated Pentagonal PyramidGyroelongated Square BipyramidGyroelongated Square PrismGyroelongated Square PyramidHeptagonal PyramidHeptahedron 4,4,4,3,3,3,3Heptahedron 5,5,5,4,4,4,3Heptahedron 6,6,4,4,4,3,3Hexagonal PrismHexagonal PyramidHexahedron 4,4,4,4,3,3Hexahedron 5,4,4,3,3,3Hexahedron 5,5,4,4,3,3Icosahedron, RegularIcosidodecahedronOblique Square PyramidOctagonal AntiprismOctahedron, RegularPentagonal AntiprismPentagonal BipyramidPentagonal CupolaPentagonal PrismPentagonal PyramidPentagonal RotundaPentagrammic PrismRectangular PyramidRhombic PrismRhombicuboctahedronRight Pentagonal Star PyramidSmall RhombidodecahedronSmall Stellated DodecahedronSnub CubeSnub DodecahedronSquare AntiprismSquare CupolaSquare PyramidSquare TrapezohedronStellated OctahedronTetrahedron - RegularTetrakis HexahedronTriakis OctahedronTriakis TetrahedronTriangular BipyramidTriangular CupolaTriangular PentahedronTriangular PrismTriangular Pyramid, ObliqueTruncated CubeTruncated CuboctahedronTruncated DodecahedronTruncated IcosahedronTruncated IcosidodecahedronTruncated OctahedronTruncated Square TrapezohedronTruncated Tetrahedron