21-110: Problem Solving in Recreational Mathematics Project Assigned Wednesday, March 17, 2010
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Art and Recreational Math Based on Kite-Tiling Rosettes
Bridges 2018 Conference Proceedings Art and Recreational Math Based on Kite-Tiling Rosettes Robert W. Fathauer Tessellations Company, Phoenix, AZ 85044, USA; [email protected] Abstract We describe here some properties of kite-tiling rosettes and the wide range of artistic and recreational mathematics uses of kite-tiling rosettes. A kite-tiling rosette is a tiling with a single kite-shaped prototile and a singular point about which the tiling has rotational symmetry. A tiling with n-fold symmetry is comprised of rings of n kites of the same size, with kite size increasing with distance away from the singular point. The prototile can be either convex or concave. Such tilings can be constructed over a wide range of kite shapes for all n > 2, and for concave kites for n = 2. A finite patch of adjacent rings of tiles can serve as a scaffolding for constructing knots and links, with strands lying along tile edges. Such patches serve as convenient templates for attractive graphic designs and Escheresque artworks. In addition, these patches can be used as grids for a variety of puzzles and games and are particularly well suited to pandiagonal magic squares. Three-dimensional structures created by giving the tiles thickness are also explored. Introduction Broadly defined, rosettes are designs or objects that are flowerlike or possess a single point of rotational symmetry. They often contain lines of mirror symmetry through the rotation center as well. Rhombus- based tiling rosettes with n-fold rotational symmetry of the type shown in Fig. 1a are relatively well known and can be constructed for any n greater than 2. -
The Potential of Recreational Mathematics to Support The
The potential of recreational mathematics to support the development of mathematical learning ROWLETT, Peter <http://orcid.org/0000-0003-1917-7458>, SMITH, Edward, CORNER, Alexander, O'SULLIVAN, David and WALDOCK, Jeff Available from Sheffield Hallam University Research Archive (SHURA) at: http://shura.shu.ac.uk/25024/ This document is the author deposited version. You are advised to consult the publisher's version if you wish to cite from it. Published version ROWLETT, Peter, SMITH, Edward, CORNER, Alexander, O'SULLIVAN, David and WALDOCK, Jeff (2019). The potential of recreational mathematics to support the development of mathematical learning. International Journal of Mathematical Education in Science and Technology, 50 (7), 972-986. Copyright and re-use policy See http://shura.shu.ac.uk/information.html Sheffield Hallam University Research Archive http://shura.shu.ac.uk The potential of recreational mathematics to support the development of mathematical learning Peter Rowletta*, Edward Smitha, Alexander S. Corner a, David O’Sullivan a and Jeff Waldock a. aDepartment of Engineering and Mathematics, Sheffield Hallam University, Sheffield, U.K. *corresponding author: [email protected] Peter Rowlett: ORCiD: https://orcid.org/0000-0003-1917-7458 Twitter: http://twitter.com/peterrowlett LinkedIn: https://www.linkedin.com/in/peterrowlett Edward Smith: ORCiD: https://orcid.org/0000-0002-8782-1869 LinkedIn: https://www.linkedin.com/in/edd-smith-53575610b/ Alexander S. Corner: ORCiD: https://orcid.org/0000-0001-6222-3443 David O'Sullivan: ORCiD: https://orcid.org/0000-0002-9192-422X LinkedIn: https://www.linkedin.com/in/david-o-sullivan-8456006a Jeff Waldock: ORCiD: https://orcid.org/0000-0001-6583-9884 LinkedIn: https://uk.linkedin.com/in/jeffwaldock The potential of recreational mathematics to support the development of mathematical learning A literature review establishes a working definition of recreational mathematics: a type of play which is enjoyable and requires mathematical thinking or skills to engage with. -
A Quarter-Century of Recreational Mathematics
A Quarter-Century of Recreational Mathematics The author of Scientific American’s column “Mathematical Games” from 1956 to 1981 recounts 25 years of amusing puzzles and serious discoveries by Martin Gardner “Amusement is one of the kamp of the University of fields of applied math.” California at Berkeley. Arti- —William F. White, cles on recreational mathe- A Scrapbook of matics also appear with in- Elementary Mathematics creasing frequency in mathe- matical periodicals. The quarterly Journal of Recrea- tional Mathematics began y “Mathemati- publication in 1968. cal Games” col- The line between entertain- Mumn began in ing math and serious math is the December 1956 issue of a blurry one. Many profes- Scientific American with an sional mathematicians regard article on hexaflexagons. their work as a form of play, These curious structures, cre- in the same way professional ated by folding an ordinary golfers or basketball stars strip of paper into a hexagon might. In general, math is and then gluing the ends to- considered recreational if it gether, could be turned inside has a playful aspect that can out repeatedly, revealing one be understood and appreci- or more hidden faces. The Gamma Liaison ated by nonmathematicians. structures were invented in Recreational math includes 1939 by a group of Princeton elementary problems with University graduate students. DONNA BISE elegant, and at times surpris- Hexaflexagons are fun to MARTIN GARDNER continues to tackle mathematical puz- ing, solutions. It also encom- play with, but more impor- zles at his home in Hendersonville, N.C. The 83-year-old writ- passes mind-bending para- tant, they show the link be- er poses next to a Klein bottle, an object that has just one sur- doxes, ingenious games, be- face: the bottle’s inside and outside connect seamlessly. -
Popularising Mathematics
Popularising Mathematics Philipp Legner August 2013 Abstract Mathematics has countless applications in science, engineering and technology, yet school mathematics is one of the most unpopular subjects, perceived as difficult, boring and not useful in life. ‘Popularisation’ projects can help bridge this gap, by showing how exciting, applicable and beautiful mathematics is. Some popularisation projects focus on telling the wider public about mathematics, including its history, philosophy and applications; other projects encourage you to actively do mathematics and discover surprising relationships and beautiful results using mathematical reasoning and thinking. In this report I will develop a framework to classify and evaluate popularisation, and analyse a wide range of existing projects – ranging from competitions to websites, movies, exhibitions, books and workshops. I also reflect upon my personal experiences in designing popularisation activities. I would like to thank Professor Dave Pratt for his advise while writing this report. Table of Contents Introduction 1 Part 1: A Framework for Mathematics Popularisation The Value of Mathematics ........................................................................... 2 Defining Mathematics Popularisation ...................................................... 4 Designing Mathematics Popularisation ................................................... 8 Evaluating Popularisation Projects ............................................................ 11 Part 2: Case Studies of Popularisation Projects -
Mathematics and Arts
Mathematics and Arts All´egoriede la G´eom´etrie A mathematical interpretation Alda Carvalho, Carlos Pereira dos Santos, Jorge Nuno Silva ISEL & Cemapre-ISEG, CEAFEL-UL, University of Lisbon [email protected] [email protected] [email protected] Abstract: In this work, we present a mathematical interpretation for the mas- terpiece All´egoriede la G´eom´etrie (1649), painted by the French baroque artist Laurent de La Hyre (1606{1656). Keywords: Laurent de La Hyre, \All´egoriede la G´eom´etrie",baroque art, mathematical interpretation, perspective. Introduction The main purpose of this text is to present a mathematical interpretation for the masterpiece All´egoriede la G´eom´etrie, from a well-known series of paint- ings, Les 7 arts lib´eraux, by the French baroque artist Laurent de La Hyre (1606{1656). Figure 1: All´egoriede la G´eom´etrie (1649), oil on canvas. Recreational Mathematics Magazine, Number 5, pp. 33{45 DOI 10.1515/rmm{2016{0003 34 allegorie´ de la geom´ etrie´ Laurent de La Hyre painted the series Les 7 arts lib´eraux between 1649 and 1650 to decorate G´ed´eonTallemant's residence. Tallemant was an adviser of Louis xiv (1638{1715). The king was 10 years old at the time of the commission. According to the artist's son, Philippe de La Hire (1640{1718), writing around 1690 [5], (. .) une maison qui appartenoit autrefois a M. Tallemant, maistre des requestes, sept tableaux repres´entant les sept arts liberaux qui font l'ornement d'une chambre. Also, Guillet de Saint-Georges, a historiographer of the Acad´emieRoyale de Peinture et de Sculpture, mentioned that it was Laurent's work for the Ca- puchin church in the Marais which led to the commission for the \Seven Liberal Arts" in a house [2]. -
Mathematical Theory of Big Game Hunting
DOCUMEWT RESUME ED 121 522 SE 020 770 AUTHOR Schaaf, Willie' L. TITLE A Bibliography of Recreational Mathematics, Volume 1. Fourth, Edition. INSTITUTION National Council of Teachers of Mathematics, Inc., Reston, Va. PUB DATE 70 NOTE 160p.; For related documents see Ed 040 874 and ED 087 631 AVAILABLE FROMNational Council of Teachers of Mathematics, Inc., 1906 Association Drive, Reston, Virginia 22091 EDRS PRICE MP-$0.83 Plus Postage. HC Not Available from EDRS. DESCRIPTORS *Annotated Bibliographies; *Games; Geometric Concepts; History; *Literature Guides; *Mathematical Enrichment; Mathematics; *Mathematics Education; Number Concepts; Reference Books ABSTRACT This book is a partially annotated bibliography of books, articles, and periodicals concerned with mathematical games, puzzles, and amusements. It is a reprinting of Volume 1 of a three-volume series. This volume, originally published in 1955, treats problems and recreations which have been important in the history of mathematics as well as some of more modern invention. The book is intended for use by both professional and amateur mathematicians. Works on recreational mathematics are listed in eight broad categories: general works, arithmetic and algebraic recreations, geometric recreations, assorted recreations, magic squares, the Pythagorean relationship, famous problems of antiquity, and aathematical 'miscellanies. (SD) *********************************************************************** Documents acquired by ERIC include many informal unpublished * materials not available from other sources. ERIC sakes every effort * * to obtain the best copy available. Nevertheless, items of marginal * * reproducibility are often encountered and this affects the quality* * of the microfiche and hardcopy reproductions ERIC aakes available * * via the ERIC Document Reproduction Service (EDRS). EDRS is not * responsible for the quality of the original document. -
The Role of Tribal Elder in Teaching Calculus Through An
THE ROLE OF TRIBAL ELDER IN TEACHING CALCULUS THROUGH AN ETHNOMATHEMATICAL LENS A DISSERTATION IN Curriculum and Instruction and Mathematics and Physics Presented to the Faculty of the University of Missouri-Kansas City in partial fulfillment of the requirements for the degree DOCTOR OF PHILOSOPHY by ROBERT RIGGS M.A., University of Missouri-Kansas City, 2003 B.A., University of Missouri-Columbia, 1983 Kansas City, Missouri 2012 © 2012 ROBERT RIGGS ALL RIGHTS RESERVED ROLE OF TRIBAL ELDER IN TEACHING CALCULUS THROUGH AN ETHNOMATHEMATICAL LENS Robert Christensen Riggs, Candidate for the Doctor of Philosophy Degree University of Missouri-Kansas City, 2012 ABSTRACT In action research study I was the classroom teacher of high school-aged African American students participating in the six-week summer portion of the Reach Up program. The purpose of Reach Up is to help students improve study skills, build confidence, motivation, self-discipline, maturity and better grades so that they can go to the college of their choice. Students selected have demonstrated academic promise, are “first-generation” college students, and have been selected from the city’s urban core high schools. This study examined the relational and instructional dynamics that took place in the classroom in which the curriculum was developed through an ethnomathematical lens. Ethnomathematics is grounded in the Freirean model of valuing the intellectual contributions of marginalized cultures and using these contributions to teach for liberation. This study introduces the culturally responsive strategy of teaching as the “Tribal Elder.” A Tribal Elder is one who is a leader in the community, who knows how to navigate the outside world to ensure survival, is related to the students by kin, and is trusted by the students and their parents. -
Recreational Mathematics
Recreational Mathematics Paul Yiu Department of Mathematics Florida Atlantic University Summer 2003 Chapters 1–44 Version 031209 ii Contents 1 Lattice polygons 101 1.1 Pick’s Theorem: area of lattice polygon . ....102 1.2 Counting primitive triangles . ...........103 1.3 The Farey sequence . ..................104 2 Lattice points 109 2.1 Counting interior points of a lattice triangle . ....110 2.2 Lattice points on a circle . ...........111 3 Equilateral triangle in a rectangle 117 3.1 Equilateral triangle inscribed in a rectangle . ....118 3.2 Construction of equilateral triangle inscribed in a rect- angle . .........................119 4 Basic geometric constructions 123 4.1 Geometric mean . ..................124 4.2 Harmonic mean . ..................125 4.3 Equal subdivisions of a segment . ...........126 4.4 The Ford circles . ..................127 5 Greatest common divisor 201 5.1 gcd(a, b) as an integer combination of a and b .....202 5.2 Nonnegative integer combinations of a and b ......203 5.3 Cassini formula for Fibonacci numbers . ....204 5.4 gcd of generalized Fibonacci and Lucas numbers ....205 6 Pythagorean triples 209 6.1 Primitive Pythagorean triples . ...........210 6.2 Primitive Pythagorean triangles with square perimeters 211 iv CONTENTS 6.3 Lewis Carroll’s conjecture on triples of equiareal Pythagorean triangles . ........................212 6.4 Points at integer distances from the sides of a primitive Pythagorean triangle . .................213 6.5 Dissecting a rectangle into Pythagorean triangles . 214 7 The tangrams 225 7.1 The Chinese tangram . .................226 7.2 A British tangram . .................227 7.3 Another British tangram .................228 8 The classical triangle centers 231 8.1 The centroid . -
Ethnomathematical Dimensions of the Shiva and Uyerver Children Plays of the Tiv People of Akor Village in Guma Local Government Area of Benue State, Nigeria
Ethnomathematical Dimensions of the Shiva and Uyerver Children Plays of the Tiv 78 People of Akor Village in Guma Local Government Area of Benue State, Nigeria VillageMath Educational Review Network for Grassroots Science and Mathematics Education (The VillageMath Network) Department of Mathematics Education Federal University of Agriculture, Makurdi, NIGERIA Volume 2, Issue 1 June , 2021 CODEN : VERIAU Ethnomathematical Dimensions of the Shiva and Uyerver Children Plays of the Tiv People of Akor Village in Guma Local Government Area of Benue State, Nigeria Jesse Aondofa ABA and Joshua Abah ABAH Department of Mathematics Education Joseph Sarwuan Tarka University, Makurdi, Nigeria DOI: 10.5281/zenodo.4957879 Article History: Received 26th May, 2021; Revised 4th June, 2021; Published 15th June, 2021. Copyright © 2021 by Author(s) and The VillageMath Network This work is licensed under Creative Commons Attribution 4.0 International (CC BY 4.0) https://creativecommons.org/licenses/by/4.0/ How to Cite this Article: Aba, J. A. & Abah, J. A. (2021). Ethnomathematical Dimensions of the Shiva and Uyerver Children Plays of the Tiv People of Akor Village in Guma Local Government Area of Benue State, Nigeria. VillageMath Educational Review (VER), 2(1) , 78-106. https://ngsme.villagemath.net/journals/ver/v2i1/aba-abah Abstract The study investigate the mathematical dimensions of the shiva and uyerver children plays of the Tiv people of Akor Village in Guma Local Government Area of Benue State, Nigeria. Six research questions and were formulated to guide the study. The study employed a phenomenological research design to achieve the objectives of the study. The study population consists of the entire population of people living in Akor village of Guma Local Government Area of Benue State. -
Ed 076 428 Author Title Institution Pub Date
DOCUMENT RESUME ED 076 428 SE 016 104 AUTHOR Schaaf, William L. TITLE The High School Mathematics Library. Fifth Edition. INSTITUTION National Council of Teachers of Mathematics,Inc., Washington, D.C. PUB DATE 73 NOTE 81p. AVAILABLE FROMNational Council of Teachers of Mathematics,1906 Association Drive, Reston, Virginia 22091($1.50) EDRS PRICE MF-$0.65 HC Not Available from EDRS. DESCRIPTORS *Annotated Bibliographies; Booklists;*Instruction; Instructional Materials; *MathematicalEnrichment; Mathematics; Mathematics Education;*Secondary School Mathematics; Teacher Education ABSTRACT The scope of this booklist includes booksfor students of.average ability, for themathematically talented, for the professional interests of mathematicsteachers, and for those concerned with general mathematics atthe junior college level. About 950 titles are listed,many with brief annotations. Starring of 200 titles indicates a priority choiceas viewed by the author. Booksare classified under topics which include popularreading, foundations of mathematics, history, recreations, mathematicscontent areas, professional books for teachers, mathematicsfor parents, dictionaries and handbooks, paperbackseries, and NCTM publications. Periodicals and journals are listed also.The appendix includes a directory of publishers. A related documentis SE 015 978. (DT) FILMED FROM BEST AVAILABLECOPY U S. DEPARTMENT OF HEALTH. EDUCATION & WELFARE OFFICE OF EOUCATION THIS DOCUMENT HAS BEEN REPRO OUCEO EXACTLY AS RECEIVED FROM THE PERSON OR ORGANIZATION OR1G INATING IT POINTS OF -
How's Your Calculus?
Puzzle Corner . Allan Gottlieb How's Your enue, Stafford Staffs ST17 OEF, England) taken as 100, what is the distance DX? has started a newsletter called Puzzle (The answer is a definite number, not a Calculus? World devoted to mechanical puzzles. formula.) Judith Longyear has suggested an in formal poll of our readers to see which OCT 5 How's your calculus? Harvey kinds of problems (chess, bridge, Elentuck asks for the area of the loop of Allan Gottlieb studied geometry, cryptarithmetic, etc.) are most Y2 = (X + 4)(X2 - X + 2Y - 4). mathematics at M.I.T. (and least) appreciated. You are all wel A noncalculus solution to this would be (S.B. 1967) and Brandeis come to respond, and significant prefer very impressive, but calculus is permitted. (A.M. 1968, Ph.D. 1973); ences will effect future problem selections. he is now Assistant Pro Several readers noted an error in the Speed Department fessor of Mathematics and published solution to NS9. That problem OCT SD 1 Ruth Duffy asks us to name a Coordinator of Computer is now reopened. word in the English language with seven Mathematics at York College of the City letters, five of which are the vowels a, e, i, University of New York. Send problems, o, and u (but not necessarily in alpha solutions, and comments to him at the Problems betical order). Department of Mathematics, York Col OCT 1 William Butler wonders how lege, Jamaica, N.Y., 11451. normal is normal (in bridge, at least): OCT SD 2 The Editor of the Review dis Conventional point counting gives four covered the following problem being dis points for each ace, three per king, two tributed as part of a tongue-in-cheek per queen, and one per jack. -
Martin Gardner Papers SC0647
http://oac.cdlib.org/findaid/ark:/13030/kt6s20356s No online items Guide to the Martin Gardner Papers SC0647 Daniel Hartwig & Jenny Johnson Department of Special Collections and University Archives October 2008 Green Library 557 Escondido Mall Stanford 94305-6064 [email protected] URL: http://library.stanford.edu/spc Note This encoded finding aid is compliant with Stanford EAD Best Practice Guidelines, Version 1.0. Guide to the Martin Gardner SC064712473 1 Papers SC0647 Language of Material: English Contributing Institution: Department of Special Collections and University Archives Title: Martin Gardner papers Creator: Gardner, Martin Identifier/Call Number: SC0647 Identifier/Call Number: 12473 Physical Description: 63.5 Linear Feet Date (inclusive): 1957-1997 Abstract: These papers pertain to his interest in mathematics and consist of files relating to his SCIENTIFIC AMERICAN mathematical games column (1957-1986) and subject files on recreational mathematics. Papers include correspondence, notes, clippings, and articles, with some examples of puzzle toys. Correspondents include Dmitri A. Borgmann, John H. Conway, H. S. M Coxeter, Persi Diaconis, Solomon W Golomb, Richard K.Guy, David A. Klarner, Donald Ervin Knuth, Harry Lindgren, Doris Schattschneider, Jerry Slocum, Charles W.Trigg, Stanislaw M. Ulam, and Samuel Yates. Immediate Source of Acquisition note Gift of Martin Gardner, 2002. Information about Access This collection is open for research. Ownership & Copyright All requests to reproduce, publish, quote from, or otherwise use collection materials must be submitted in writing to the Head of Special Collections and University Archives, Stanford University Libraries, Stanford, California 94304-6064. Consent is given on behalf of Special Collections as the owner of the physical items and is not intended to include or imply permission from the copyright owner.