Showing papers in "The Mathematical Gazette in 1973"
4,285 citations
1,097 citations
TL;DR: In this article, a frieze is defined as a horizontal band of decoration around a building, and it is a pattern drawn on an infinitely long band (if you want some kind of precision, imagine the set R× [0, 1], which is the set of points (x, y) in the plane where 0 ≤ y ≤ 1), that has a certain kind of symmetry.
Abstract: First, a lesson in architecture. A frieze is a horizontal band of decoration around a building. These are some friezes from buildings in Ancient Persepolis. Note how they feature symmetrical, repeating patterns, and it is easy to see how you could keep drawing them to the left or the right, infinitely far. In mathematics, a frieze pattern will be a pattern drawn on an infinitely long band (if you want some kind of precision, imagine the set R× [0, 1], which is the set of points (x, y) in the plane where 0 ≤ y ≤ 1), that has a certain kind of symmetry.
211 citations
174 citations
83 citations
52 citations
46 citations
37 citations
TL;DR: In this article, the authors present the 2019 version of the Harvey Mudd College Instructors' Resource Manual (IMRMS) and discuss the shortcomings of the manual and its shortcomings.
Abstract: Instructors’ Resource Manual Harvey Mudd College Instructors’ Resource Manual By Michael Starbird Francis Su November 19, 2019.
TL;DR: In this paper, the authors describe four regular compounds of dodecahedra and two of small stellated icosahedra, which are regular in the sense that any vertex or face of the compound can be interchanged with any other vertex and face by a rotation or reflection of the whole compound.
Abstract: It is well known that the simpler regular solids can be assembled into compounds which have, as a whole, the symmetry of a more complicated solid: two tetrahedra with a symmetry of a cube, five cubes with that of a dodecahedron, and so forth ([1] p 134, [2] p 134) The reader may well have wondered whether any compounds of dodecahedra or icosahedra exist which are in any sense regular compounds In this article we shall describe four regular compounds, not, it is true, of dodecahedra, but of great dodecahedra and small stellated dodecahedra ([1] pp 144-5, [2] pp 90-4) Two of these compounds seem to be hitherto unknown, and the other two are published only in now obscure nineteenth-century German journals ([3], [4]) These are regular in the sense that any vertex or face of the compound can be interchanged with any other vertex or face by a rotation or reflection of the whole compound As stepping-stones on our path to these compounds we shall construct two compounds of icosahedra which do not have the property We illustrate one of these in Fig 2, which has been shaded to show that both of the icosahedra have twelve faces of one sort and eight of a second sort The sets of eight combine to form eight stars, each of which is composed of two triangles The stars are not regular hexagrams