| 单词 | regular polygon |
| 例句 | The Pythagoreans were fascinated by the regular solids, symmetrical three-dimensional objects all of whose sides are the same regular polygon. Cosmos 1980-01-01T00:00:00Z There were known to be five regular or “platonic” solids, whose sides were regular polygons, as known to the ancient Greek mathematicians after the time of Pythagoras. Cosmos 1980-01-01T00:00:00Z There are an infinite number of regular polygons, but only five regular solids. Cosmos 1980-01-01T00:00:00Z But when presented with regular polygons, their performance collapsed. Is Geometry a Language That Only Humans Know? 2022-03-22T04:00:00Z The main reason to study it is that it's, in some sense, the "next-simplest" regular polygon after the square — after all, a square has 4 sides and a pentagon has 5. Diana Davis’s Beautiful Pentagons 2020-05-23T04:00:00Z Here, the faces are still regular polygons—equilateral triangles, squares, regular pentagons, and so on—but they will mix two or more shapes together. A Few of My Favorite Spaces: The Pseudo-Rhombicuboctahedron 2018-03-31T04:00:00Z These are the five convex polyhedra—tetrahedron, cube, octahedron, dodecahedron, and icosahedron—that are made of congruent regular polygons. Justin Curry's Favorite Theorem 2017-12-09T05:00:00Z The pieces must be regular polygons, with all sides the same length and all angles equal. With Snowflakes and Unicorns, Marina Ratner and Maryam Mirzakhani Explored a Universe in Motion 2017-08-07T04:00:00Z A pamphlet explains regular polygons and Platonic, Johnson and Archimedean solids. All I Want for Christmas Is Dinosaur Dung 2012-11-21T19:15:00.253Z Hero’s expressions for the areas of regular polygons of from 5 to 12 sides in terms of the squares of the sides show interesting approximations to the values of trigonometrical ratios. Encyclopaedia Britannica, 11th Edition, Volume 13, Slice 4 "Hero" to "Hindu Chronology" 2012-04-04T02:00:56.447Z Both are convex solids made from regular polygons, and in both of them, each vertex is surrounded by three squares and a triangle. A Few of My Favorite Spaces: The Pseudo-Rhombicuboctahedron 2018-03-31T04:00:00Z The perpendicular from the center to one of the sides of a regular polygon. Webster's Unabridged Dictionary 2012-03-24T02:00:23.513Z For finding the lengths of the sides of regular polygons, scales, such as shown in Figs. Modern Machine-Shop Practice, Volumes I and II 2012-03-23T02:00:33.140Z Still more elaborate designs, based chiefly upon the square and circle, are shown in the window traceries on page 225, and others will be given in connection with the study of the regular polygons. The Teaching of Geometry 2011-10-12T02:00:52.133Z This shows that regular polygons of 7, 9, 13 sides cannot thus be constructed, but that a regular polygon of 17 sides is possible; for 17 = 24 + 1. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z He begins with a function having a graph in the form of a regular polygon, and interpolates additional angular points in an ordered sequence without limit. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 3 "Frost" to "Fyzabad" 2011-08-15T02:00:28.473Z It is a regular polygon with five bastions, founded by Frederick III. about 1662-1663. Encyclopaedia Britannica, 11th Edition, Volume 7, Slice 3 "Convention" to "Copyright" The fourth book deals with the circle in its relations to inscribed and circumscribed triangles, quadrilaterals and regular polygons. Encyclopaedia Britannica, 11th Edition, Volume 6, Slice 4 "Cincinnatus" to "Cleruchy" Book V treats of regular polygons and circles, and includes the computation of the approximate value of π. The Teaching of Geometry 2011-10-12T02:00:52.133Z Euclid considers the regular polygons of 4, 5, 6 and 15 sides. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z The rectangle under this doubled segment and the radius is equal to the square of the side of an inscribed regular polygon of 20 sides. A Budget of Paradoxes, Volume II A regular polygon, having twelve sides and as many angles. The Sailor's Word-Book An Alphabetical Digest of Nautical Terms, including Some More Especially Military and Scientific, but Useful to Seamen; as well as Archaisms of Early Voyagers, etc. A regular polygon is one the sides of which are all of an equal length. Mechanical Drawing Self-Taught It opens with a definition of a regular polygon as one that is both equilateral and equiangular. The Teaching of Geometry 2011-10-12T02:00:52.133Z Of those for which this is possible the regular polygons, i.e. polygons which have all their sides and angles equal, are the most interesting. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z This he does by inscribing and circumscribing regular polygons of 96 sides and calculating approximately their respective perimeters. The Legacy of Greece Essays By: Gilbert Murray, W. R. Inge, J. Burnet, Sir T. L. Heath, D'arcy W. Thompson, Charles Singer, R. W. Livingston, A. Toynbee, A. E. Zimmern, Percy Gardner, Sir Reginald Blomfield Apothegm.—The perpendicular line A from the center to one side of a regular polygon. Carpentry for Boys In a Simple Language, Including Chapters on Drawing, Laying Out Work, Designing and Architecture With 250 Original Illustrations The angles of regular polygons are designated by their degrees of angle, "at the centre" and "at the circumference." Mechanical Drawing Self-Taught While in elementary geometry the only regular polygons studied are convex, it is interesting to a class to see that there are also regular cross polygons. The Teaching of Geometry 2011-10-12T02:00:52.133Z We conclude with a few theorems about regular polygons which are not given by Euclid. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z It is built on the plan of a regular polygon of nine sides. God Passes By This was done, for instance, by Gauss when he found a necessary and sufficient condition that a regular polygon of a prime number of sides can be constructed by elementary methods. Popular Science Monthly Oct, Nov, Dec, 1915 — Volume 86 The angles of regular polygons: Trigon, at the centre, 120°, at the circumference, 60°. Mechanical Drawing Self-Taught The third is the somewhat interesting but mathematically unimportant application of the regular polygons to geometric design. The Teaching of Geometry 2011-10-12T02:00:52.133Z The straight lines bisecting the angles in the regular polygon meet in the same point. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z Her hull framework in section formed a regular polygon of seventeen sides, and was built up of triangular aluminium girders. British Airships, Past, Present, and Future A. Polygons; those that have their sides and angles equal we would call regular polygons. The Infant System For Developing the Intellectual and Moral Powers of all Children, from One to Seven years of Age These several conditions ought to result in a geometrically ordered dwelling, having a regular polygon as an opening. The Life of the fly; with which are interspersed some chapters of autobiography His Book IV is devoted to the construction of certain regular polygons, and his propositions on this subject are now embodied in Book V as it is usually taught in America. The Teaching of Geometry 2011-10-12T02:00:52.133Z Hence we can divide a circumference into 2n equal parts as soon as it has been divided into n equal parts, or as soon as a regular polygon of n sides has been constructed. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z Just as we may produce the sides of a regular polygon and form a regular cross polygon or stellar polygon, so we may have stellar polyhedrons. The Teaching of Geometry 2011-10-12T02:00:52.133Z Of these regular polygons two are of special interest, and these will now be considered. The Teaching of Geometry 2011-10-12T02:00:52.133Z It is possible to start with any regular polygon of which the side can conveniently be found in terms of the radius. The Teaching of Geometry 2011-10-12T02:00:52.133Z The fact that we may use for tiles on a floor three regular polygons—the triangle, square, and hexagon—is noteworthy, a fact that Proclus tells us was recognized by Pythagoras. The Teaching of Geometry 2011-10-12T02:00:52.133Z Euclid shows how to construct regular polygons of 3, 4, 5 and 15 sides. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z This point is the centre of the circles circumscribed about and inscribed in the regular polygon. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z The straight lines perpendicular to and bisecting the sides of any regular polygon meet in a point. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z Three regular polygons of six or more sides cannot form a solid angle. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z In connection with the study of the regular polygons some interest attaches to the reference to various forms of decorative design. The Teaching of Geometry 2011-10-12T02:00:52.133Z Till the beginning of the 19th century nothing was added to the knowledge of regular polygons as given by Euclid. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z |
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