1970-2011.3 TOPIC INDEX for the College Mathematics Journal (Including the Two Year College Mathematics Journal)
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Pentagonal Pyramid
Chapter 9 Surfaces and Solids Copyright © Cengage Learning. All rights reserved. Pyramids, Area, and 9.2 Volume Copyright © Cengage Learning. All rights reserved. Pyramids, Area, and Volume The solids (space figures) shown in Figure 9.14 below are pyramids. In Figure 9.14(a), point A is noncoplanar with square base BCDE. In Figure 9.14(b), F is noncoplanar with its base, GHJ. (a) (b) Figure 9.14 3 Pyramids, Area, and Volume In each space pyramid, the noncoplanar point is joined to each vertex as well as each point of the base. A solid pyramid results when the noncoplanar point is joined both to points on the polygon as well as to points in its interior. Point A is known as the vertex or apex of the square pyramid; likewise, point F is the vertex or apex of the triangular pyramid. The pyramid of Figure 9.14(b) has four triangular faces; for this reason, it is called a tetrahedron. 4 Pyramids, Area, and Volume The pyramid in Figure 9.15 is a pentagonal pyramid. It has vertex K, pentagon LMNPQ for its base, and lateral edges and Although K is called the vertex of the pyramid, there are actually six vertices: K, L, M, N, P, and Q. Figure 9.15 The sides of the base and are base edges. 5 Pyramids, Area, and Volume All lateral faces of a pyramid are triangles; KLM is one of the five lateral faces of the pentagonal pyramid. Including base LMNPQ, this pyramid has a total of six faces. The altitude of the pyramid, of length h, is the line segment from the vertex K perpendicular to the plane of the base. -
If Two Polygons Are Similar, Then Their Areas Are Proportional to the Square of the Scale Factor SOLUTION: Between Them
Chapter 10 Study Guide and Review State whether each sentence is true or false. If 6. The measure of each radial angle of a regular n-gon false, replace the underlined term to make a is . true sentence. 1. The center of a trapezoid is the perpendicular SOLUTION: distance between the bases. false; central SOLUTION: ANSWER: false; height false; central ANSWER: 7. The apothem of a polygon is the perpendicular false; height distance between any two parallel bases. 2. A slice of pizza is a sector of a circle. SOLUTION: false; height of a parallelogram SOLUTION: true ANSWER: false; height of a parallelogram ANSWER: true 8. The height of a triangle is the length of an altitude drawn to a given base. 3. The center of a regular polygon is the distance from the middle to the circle circumscribed around the SOLUTION: polygon. true SOLUTION: ANSWER: false; radius true ANSWER: 9. Explain how the areas of two similar polygons are false; radius related. 4. The segment from the center of a square to the SOLUTION: corner can be called the radius of the square. If two polygons are similar, then their areas are proportional to the square of the scale factor SOLUTION: between them. true ANSWER: ANSWER: If two polygons are similar, then their areas are true proportional to the square of the scale factor 5. A segment drawn perpendicular to a side of a regular between them. polygon is called an apothem of the polygon. SOLUTION: true ANSWER: true eSolutions Manual - Powered by Cognero Page 1 Chapter 10 Study Guide and Review 10. -
Interview with Martin Gardner Page 602
ISSN 0002-9920 of the American Mathematical Society june/july 2005 Volume 52, Number 6 Interview with Martin Gardner page 602 On the Notices Publication of Krieger's Translation of Weil' s 1940 Letter page 612 Taichung, Taiwan Meeting page 699 ., ' Martin Gardner (see page 611) AMERICAN MATHEMATICAL SOCIETY A Mathematical Gift, I, II, Ill The interplay between topology, functions, geometry, and algebra Shigeyuki Morita, Tokyo Institute of Technology, Japan, Koji Shiga, Yokohama, Japan, Toshikazu Sunada, Tohoku University, Sendai, Japan and Kenji Ueno, Kyoto University, Japan This three-volume set succinctly addresses the interplay between topology, functions, geometry, and algebra. Bringing the beauty and fun of mathematics to the classroom, the authors offer serious mathematics in an engaging style. Included are exercises and many figures illustrating the main concepts. It is suitable for advanced high-school students, graduate students, and researchers. The three-volume set includes A Mathematical Gift, I, II, and III. For a complete description, go to www.ams.org/bookstore-getitem/item=mawrld-gset Mathematical World, Volume 19; 2005; 136 pages; Softcover; ISBN 0-8218-3282-4; List US$29;AII AMS members US$23; Order code MAWRLD/19 Mathematical World, Volume 20; 2005; 128 pages; Softcover; ISBN 0-8218-3283-2; List US$29;AII AMS members US$23; Order code MAWRLD/20 Mathematical World, Volume 23; 2005; approximately 128 pages; Softcover; ISBN 0-8218-3284-0; List US$29;AII AMS members US$23; Order code MAWRLD/23 Set: Mathematical World, Volumes 19, 20, and 23; 2005; Softcover; ISBN 0-8218-3859-8; List US$75;AII AMS members US$60; Order code MAWRLD-GSET Also available as individual volumes .. -
Linking Together Members of the Mathematical Carlos Rocha, University of Lisbon; Jean Taylor, Cour- Community from the US and Abroad
NEWSLETTER OF THE EUROPEAN MATHEMATICAL SOCIETY Features Epimorphism Theorem Prime Numbers Interview J.-P. Bourguignon Societies European Physical Society Research Centres ESI Vienna December 2013 Issue 90 ISSN 1027-488X S E European M M Mathematical E S Society Cover photo: Jean-François Dars Mathematics and Computer Science from EDP Sciences www.esaim-cocv.org www.mmnp-journal.org www.rairo-ro.org www.esaim-m2an.org www.esaim-ps.org www.rairo-ita.org Contents Editorial Team European Editor-in-Chief Ulf Persson Matematiska Vetenskaper Lucia Di Vizio Chalmers tekniska högskola Université de Versailles- S-412 96 Göteborg, Sweden St Quentin e-mail: [email protected] Mathematical Laboratoire de Mathématiques 45 avenue des États-Unis Zdzisław Pogoda 78035 Versailles cedex, France Institute of Mathematicsr e-mail: [email protected] Jagiellonian University Society ul. prof. Stanisława Copy Editor Łojasiewicza 30-348 Kraków, Poland Chris Nunn e-mail: [email protected] Newsletter No. 90, December 2013 119 St Michaels Road, Aldershot, GU12 4JW, UK Themistocles M. Rassias Editorial: Meetings of Presidents – S. Huggett ............................ 3 e-mail: [email protected] (Problem Corner) Department of Mathematics A New Cover for the Newsletter – The Editorial Board ................. 5 Editors National Technical University Jean-Pierre Bourguignon: New President of the ERC .................. 8 of Athens, Zografou Campus Mariolina Bartolini Bussi GR-15780 Athens, Greece Peter Scholze to Receive 2013 Sastra Ramanujan Prize – K. Alladi 9 (Math. Education) e-mail: [email protected] DESU – Universitá di Modena e European Level Organisations for Women Mathematicians – Reggio Emilia Volker R. Remmert C. Series ............................................................................... 11 Via Allegri, 9 (History of Mathematics) Forty Years of the Epimorphism Theorem – I-42121 Reggio Emilia, Italy IZWT, Wuppertal University [email protected] D-42119 Wuppertal, Germany P. -
OF the AMERICAN MATHEMATICAL SOCIETY 157 Notices February 2019 of the American Mathematical Society
ISSN 0002-9920 (print) ISSN 1088-9477 (online) Notices ofof the American MathematicalMathematical Society February 2019 Volume 66, Number 2 THE NEXT INTRODUCING GENERATION FUND Photo by Steve Schneider/JMM Steve Photo by The Next Generation Fund is a new endowment at the AMS that exclusively supports programs for doctoral and postdoctoral scholars. It will assist rising mathematicians each year at modest but impactful levels, with funding for travel grants, collaboration support, mentoring, and more. Want to learn more? Visit www.ams.org/nextgen THANK YOU AMS Development Offi ce 401.455.4111 [email protected] A WORD FROM... Robin Wilson, Notices Associate Editor In this issue of the Notices, we reflect on the sacrifices and accomplishments made by generations of African Americans to the mathematical sciences. This year marks the 100th birthday of David Blackwell, who was born in Illinois in 1919 and went on to become the first Black professor at the University of California at Berkeley and one of America’s greatest statisticians. Six years after Blackwell was born, in 1925, Frank Elbert Cox was to become the first Black mathematician when he earned his PhD from Cornell University, and eighteen years later, in 1943, Euphemia Lofton Haynes would become the first Black woman to earn a mathematics PhD. By the late 1960s, there were close to 70 Black men and women with PhDs in mathematics. However, this first generation of Black mathematicians was forced to overcome many obstacles. As a Black researcher in America, segregation in the South and de facto segregation elsewhere provided little access to research universities and made it difficult to even participate in professional societies. -
Humanizing Mathematics and Its Philosophy
Bharath Sriraman Editor Humanizing Mathematics and its Philosophy Essays Celebrating the 90th Birthday of Reuben Hersh Bharath Sriraman Editor Humanizing Mathematics and its Philosophy Essays Celebrating the 90th Birthday of Reuben Hersh Editor Bharath Sriraman Department of Mathematical Sciences The University of Montana Missoula, MT, USA ISBN 978-3-319-61230-0 ISBN 978-3-319-61231-7 (eBook) DOI 10.1007/978-3-319-61231-7 Library of Congress Control Number: 2017958868 © Springer International Publishing AG 2017 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. -
Areas of Regular Polygons Finding the Area of an Equilateral Triangle
Areas of Regular Polygons Finding the area of an equilateral triangle The area of any triangle with base length b and height h is given by A = ½bh The following formula for equilateral triangles; however, uses ONLY the side length. Area of an equilateral triangle • The area of an equilateral triangle is one fourth the square of the length of the side times 3 s s A = ¼ s2 s A = ¼ s2 Finding the area of an Equilateral Triangle • Find the area of an equilateral triangle with 8 inch sides. Finding the area of an Equilateral Triangle • Find the area of an equilateral triangle with 8 inch sides. 2 A = ¼ s Area3 of an equilateral Triangle A = ¼ 82 Substitute values. A = ¼ • 64 Simplify. A = • 16 Multiply ¼ times 64. A = 16 Simplify. Using a calculator, the area is about 27.7 square inches. • The apothem is the F height of a triangle A between the center and two consecutive vertices H of the polygon. a E G B • As in the activity, you can find the area o any regular n-gon by dividing D C the polygon into congruent triangles. Hexagon ABCDEF with center G, radius GA, and apothem GH A = Area of 1 triangle • # of triangles F A = ( ½ • apothem • side length s) • # H of sides a G B = ½ • apothem • # of sides • side length s E = ½ • apothem • perimeter of a D C polygon Hexagon ABCDEF with center G, This approach can be used to find radius GA, and the area of any regular polygon. apothem GH Theorem: Area of a Regular Polygon • The area of a regular n-gon with side lengths (s) is half the product of the apothem (a) and the perimeter (P), so The number of congruent triangles formed will be A = ½ aP, or A = ½ a • ns. -
Proving Is Convincing and Explaining
REUBEN HERSH PROVING IS CONVINCING AND EXPLAINING ABSTRACT. In mathematical research, the purpose of proof is to convince. The test of whether something is a proof is whether it convinces qualified judges. In the classroom, on the other hand, the purpose of proof is to explain. Enlightened use of proofs in the mathematics classroom aims to stimulate the students' understanding, not to meet abstract standards of "rigor" or "honesty." I. WHAT IS PROOF? This is one question we mathematics teachers and students would normally never think of asking. We've seen proofs, we've done proofs. Proof is what we've been watching and doing for 10 or 20 years! In the Mathematical Experience (Davis and Hersh, 1981, pp. 39-40) this almost unthinkable question is asked of the Ideal Mathematician (the I.M. - the most mathematician-like mathematician) by a student of philosophy: "What is a mathematical proof?" The I.M. responds with examples - the Fundamental Theorem of This, the Fundamental Theorem of That. But the philosophy student wants a general definition, not just some examples. The I.M. tells the philosophy student about proof as it's portrayed in formal logic: permutation of logical symbols according to certain formal rules. But the philosophy student has seen proofs in mathematics classes, and none of them fit this description. The Ideal Mathematician crumbles. He confides that formal logic is rarely employed in proving theorems, that the real truth of the matter is that a proof is just a convincing argument, as judged by competent judges. The philosophy student is appalled by this betrayal of logical standards. -
Influence of Coal Dust on Premixed Turbulent Methane-Air Flames Scott
Influence of Coal Dust on Premixed Turbulent Methane-Air Flames Scott R. Rockwell A Dissertation Submitted to the Faculty of Worcester Polytechnic Institute In partial fulfillment of the requirements for the Degree of Doctor of Philosophy in Fire Protection Engineering July 2012 APPROVED: _____________________________________________ Professor Ali S. Rangwala, Advisor _____________________________________________ Professor Kathy A. Notarianni, Head of Department _____________________________________________ Professor Simon W. Evans _____________________________________________ Professor Sanjeeva Balasuriya _____________________________________________ Dr. Alfonso F. Ibarreta _____________________________________________ Professor Forman A. Williams Table of Contents Table of Contents ............................................................................................................................ 2 List of figures .................................................................................................................................. 5 List of tables .................................................................................................................................... 6 Nomenclature .................................................................................................................................. 7 Acknowledgments........................................................................................................................... 8 Abstract .......................................................................................................................................... -
NRC Aiming for June Launch of Education Board
THE NEWSLETTER OF THE MATHEMATICAL ASSOCIATION OF AMERICA VOLUME 5NUMBER3 MAY-JUNE 1985 NRC Aiming for June Launch of Education Board he National Research Council (NRC) of the National The purpose of the Board, which will report directly to the Academy of Sciences is aiming for a June 1985 launch leadership of the National Research Council, is to provide a Tdate for its new Board on Mathematical Sciences Edu continuing national capability to assess and support edu cation. [See FOCUS, March-April 1985.] cational conditions and needs in the area of mathematical A major step in this direction was taken on April 12-13, sciences education across the country. NRC hopes the Board when the NRC called a meeting of some 50 mathematical will be a practical response to present problems in devel scientists, educators, and administrators to discuss the pre oping quality instruction in mathematical sciences educa liminary plans for the composition, funding, and projects of tion. The Board's activities will be designed to provide advice the Board. Meeting participants included MAA President Lynn and insight to users across the country who seek to rebuild A. Steen; F. Joe Crosswhite, President, National Council of the quality of mathematical sciences education. Teachers of Mathematics; Gordon M. Ambach, President, Key issues in precollege mathematical sciences education Council of Chief State School Officers; and Bassam Z. Shak which have been identified for early action by the Board are hashiri, Assistant Director, Science and Engineering Edu testing, curriculum guidelines, staff development, commu cation Directorate of the National Science Foundation. The nication and dissemination, and computer-enhanced math meeting was chaired by James Ebert, President of the Car ematics education. -
HW – Areas of Regular Polygons
Name _____ Date Period HW – Areas of Regular Polygons In a regular polygon, a segment drawn from the center of the polygon perpendicular to a side of the polygon is called an apothem. In the figure at the right, PS is an apothem. If a regular polygon has an area of A square units, a perimeter of P units, and an apothem of a units, then A = or A = Example: Find the area of a regular pentagon with an apothem of 2.8 cm and a perimeter of 20.34 cm. A = Area of a regular polygon A = (20.34)(2.8) A = 28.476 The area is 28.476 square centimeters. Find the area of each regular polygon described. Round your answers to the nearest tenth. 1. a hexagon with an apothem of 8.7 cm and 2. a pentagon with a perimeter of 54.49 m and sides that are each 10 cm long an apothem of 7.5 m 3. A regular octagon with an apothem 4.8 4. A square with a side 24 inches long and an centimeters long and a side 4 centimeters apothem 12 inches long long Find the apothem for each of the regular polygons below. Then find the perimeter and area for each figure. 5. 6. 7. a ________ a ________ a ________ P = ________ P = ________ P = ________ A ________ A ________ A ________ 8. The perimeter of a regular hexagon is 48 ft. 9. Ms. King wants to add a triangular deck in What is the area of this polygon? the yard behind her house. -
1970-2020 TOPIC INDEX for the College Mathematics Journal (Including the Two Year College Mathematics Journal)
1970-2020 TOPIC INDEX for The College Mathematics Journal (including the Two Year College Mathematics Journal) prepared by Donald E. Hooley Emeriti Professor of Mathematics Bluffton University, Bluffton, Ohio Each item in this index is listed under the topics for which it might be used in the classroom or for enrichment after the topic has been presented. Within each topic entries are listed in chronological order of publication. Each entry is given in the form: Title, author, volume:issue, year, page range, [C or F], [other topic cross-listings] where C indicates a classroom capsule or short note and F indicates a Fallacies, Flaws and Flimflam note. If there is nothing in this position the entry refers to an article unless it is a book review. The topic headings in this index are numbered and grouped as follows: 0 Precalculus Mathematics (also see 9) 0.1 Arithmetic (also see 9.3) 0.2 Algebra 0.3 Synthetic geometry 0.4 Analytic geometry 0.5 Conic sections 0.6 Trigonometry (also see 5.3) 0.7 Elementary theory of equations 0.8 Business mathematics 0.9 Techniques of proof (including mathematical induction 0.10 Software for precalculus mathematics 1 Mathematics Education 1.1 Teaching techniques and research reports 1.2 Courses and programs 2 History of Mathematics 2.1 History of mathematics before 1400 2.2 History of mathematics after 1400 2.3 Interviews 3 Discrete Mathematics 3.1 Graph theory 3.2 Combinatorics 3.3 Other topics in discrete mathematics (also see 6.3) 3.4 Software for discrete mathematics 4 Linear Algebra 4.1 Matrices, systems