Dice Problems Navajo Math Camp July 26-30 2021 History of Dice Precursors of Dice

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Dice problems Navajo Math Camp July 26-30 2021 History of dice Precursors of dice: Astragals, the anklebones of sheep, buffalo, or other animals; casting lots to divine the future Greek and Roman times: dice made of different materials Cubical dice: in Chinese excavations from 600 bce and in Egyptian tombs dating from 2000 bce Equal faces? In how many ways can you arrange three dice side by side on a surface so that the sum of the number of pips on each of the four faces (top, bottom, front and back) is equal? from https://nrich.maths.org/ (great resource for problems, games and activities) How many dice? Carol rolled a large handful of six-sided dice. The total of all the numbers Carol got was 521. After some calculating, Carol worked out that the probability that of her total being 521 was the same as the probability that her total being 200. How many dice did Carol roll? Magic with dice You are blindfolded and told that on the right side of the table there are 6 dice with pips showing that sum to 16 and on the left side of the table there are 6 dice that sum to 19. Your task is to create two groups of dice that have the same sum while still blindfolded! Perudo 5 dice each player - you see what you roll, but the others don’t; Take turns, bids must go up: Bid 26 means that you think that there are at least two sixes; 34 means ‘at least three fours’; after 26 you could not bid e.g., 15 (at least one five) because 15 < 26 You can also call bluff on the previous player Lose a die if your bluff is called or if you wrongly call bluff; last person with a die wins (figure by Gord Hamilton - K12 Unsolved Problems) Balanced dice d4 - truncated tetrahedron d8 - truncated octahedron d12 - rhombic dodecahedron d24 - deltoidal icositetrahedron d60 - deltoidal hexecontahedron d120 https://mathigon.org/polypad The Dice Lab How to do it? Opposite sides: add up to one more than the number of sides of the die (6+1=7 with normal die) Vertex sums Face sums The idea is to try to balance these sums as much as possible with many sided dice (d12, d20, d64, d120) Linear programming.

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Are Your Polyhedra the Same As My Polyhedra?
Are Your Polyhedra the Same as My Polyhedra? Branko Grünbaum 1 Introduction “Polyhedron” means different things to different people. There is very little in common between the meaning of the word in topology and in geometry. But even if we confine attention to geometry of the 3-dimensional Euclidean space – as we shall do from now on – “polyhedron” can mean either a solid (as in “Platonic solids”, convex polyhedron, and other contexts), or a surface (such as the polyhedral models constructed from cardboard using “nets”, which were introduced by Albrecht Dürer [17] in 1525, or, in a more mod- ern version, by Aleksandrov [1]), or the 1-dimensional complex consisting of points (“vertices”) and line-segments (“edges”) organized in a suitable way into polygons (“faces”) subject to certain restrictions (“skeletal polyhedra”, diagrams of which have been presented first by Luca Pacioli [44] in 1498 and attributed to Leonardo da Vinci). The last alternative is the least usual one – but it is close to what seems to be the most useful approach to the theory of general polyhedra. Indeed, it does not restrict faces to be planar, and it makes possible to retrieve the other characterizations in circumstances in which they reasonably apply: If the faces of a “surface” polyhedron are sim- ple polygons, in most cases the polyhedron is unambiguously determined by the boundary circuits of the faces. And if the polyhedron itself is without selfintersections, then the “solid” can be found from the faces. These reasons, as well as some others, seem to warrant the choice of our approach.
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Dictionary of Mathematics
Dictionary of Mathematics English – Spanish | Spanish – English Diccionario de Matemáticas Inglés – Castellano | Castellano – Inglés Kenneth Allen Hornak Lexicographer © 2008 Editorial Castilla La Vieja Copyright 2012 by Kenneth Allen Hornak Editorial Castilla La Vieja, c/o P.O. Box 1356, Lansdowne, Penna. 19050 United States of America PH: (908) 399-6273 e-mail: [email protected] All dictionaries may be seen at: http://www.EditorialCastilla.com Sello: Fachada de la Universidad de Salamanca (ESPAÑA) ISBN: 978-0-9860058-0-0 All rights reserved. No part of this book may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording or by any informational storage or retrieval system without permission in writing from the author Kenneth Allen Hornak. Reservados todos los derechos. Quedan rigurosamente prohibidos la reproducción de este libro, el tratamiento informático, la transmisión de alguna forma o por cualquier medio, ya sea electrónico, mecánico, por fotocopia, por registro u otros medios, sin el permiso previo y por escrito del autor Kenneth Allen Hornak. ACKNOWLEDGEMENTS Among those who have favoured the author with their selfless assistance throughout the extended period of compilation of this dictionary are Andrew Hornak, Norma Hornak, Edward Hornak, Daniel Pritchard and T.S. Gallione. Without their assistance the completion of this work would have been greatly delayed. AGRADECIMIENTOS Entre los que han favorecido al autor con su desinteresada colaboración a lo largo del dilatado período de acopio del material para el presente diccionario figuran Andrew Hornak, Norma Hornak, Edward Hornak, Daniel Pritchard y T.S. Gallione. Sin su ayuda la terminación de esta obra se hubiera demorado grandemente.
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Measuring Sphericity a Measure of the Sphericity of a Convex Solid Was Introduced by G
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