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Group Activities for Math Enthusiasts
Abstract
In this article we present three group activities designed for math students: a balloon-twisting workshop, a group proof of the irrationality of π, and a game of Math Bingo. These activities have been particularly successful in building enthusiasm for mathematics and camaraderie among math faculty and students at Kenyon College.
Sonia Kovalevsky Days (SK Days) are nationally-held outreach events that are commonly organized by local chapters of the Association for Women in Mathematics (AWM) to encourage young women to continue their study of mathematics. The AWM Student Chapter at Worcester Polytechnic Institute hosted virtual renditions of SK Day for middle school girls in Spring 2020 and 2021. This paper discusses the implementation of these events, including the virtual program logistics and five interactive online mathematics activities. Participant feedback suggests a successful transition from an in-person to online format of SK Day, with benefits to both the middle school participants and the undergraduate student volunteers. The activities and online resources described in this article have the potential to be utilized in future hybrid outreach events.
Let π=a/b, the quotient of positive integers. We define the polynomials
\begin{gathered}
f(x) = \frac{{{x^n}{{(a - bx)}^n}}}{{n!}} \hfill \\
F(x) = f(x) - {f^{(2)}}(x) + {f^{(4)}} - ... + {( - 1)^n}{f^{(2n)}}(x) \hfill \\
\end{gathered}
the positive integer n being specified later. Since n!f(x)has integral coefficients and terms in x of degree not less than n, f(x) and its derivatives f
(i)(x) have integral values for x=0; also for x=π=a/b, since f(x) =f(a/b–x). By elementary calculus we have
and
\int_0^\pi {f(x)\sin xdx} = \left[ {F'(x)\sin x - F(x)\cos x} \right]_0^\pi F(x) + F(0)
Démontrer que le diametre du cercle n’eft point à fa circonférence comme un nombre entier à un nombre entier, c’eft là une chofe, dont les géometres ne feront gueres furpris. On connoit les nombres de Ludolph, les rapports trouvés par Archimede, par Metius etc. de même qu’un grand nombre de fuites infinies, qui toutes fe rapportent à la quadrature du cercle. Et fi la Comme dc ces fuites eft une quantité rationelle, on doit affez naturellement conclure, qu’elle fera ou un nombre entier, ou une fraction très fimpie. Car, s’il y falloit une frashion fort compofée, quelle raifon y auroit-il, pourquoi plutôt telle que telle autre quelconque? C’eft ainfi, par exemple, que la tomme de la fuite
This paper is a reference for a hands-on workshop where participants will make polyhedra out of balloons, and learn how to use balloons to demonstrate mathematical principals, from preschool (counting, shape recognition) to college level (graph theory, theoretical computer science). Balloons are a great medium for teaching hands-on mathematics, whether to young students, who are more open to the idea that an octahedron (for example) is a beautiful object if it is made out of a balloon, to adults, who can find an interesting challenge in constructing complicated models. Balloons are also inexpensive, easy to obtain, and easy to work with (once you learn the basics, which will be covered in the workshop), which combined with their hands-on nature and visual appeal make them a great medium for teaching and learning mathematics.
Balloon polyhedra Shaping Space: A Polyhedral Approach
- E D Demaine
- M L Demaine
- V Hart
Pi is irrational. http://hhr-m.userweb.mwn
- H Richter
40 One must be under this age to win the Fields Medal [K] 41 A prime p famous for producing primes via the polynomial f ðxÞ ¼ x 2 þ x þ p (f produces a prime for all À 41 < x < 41 ) [K] 42 The alphanumeric value of
- Bernhard Riemannk
39 Bernhard Riemann's age when he died [K]
40 One must be under this age to win the Fields Medal [K]
41 A prime p famous for producing primes via the polynomial f ðxÞ ¼ x 2 þ x þ p (f
produces a prime for all À 41 < x < 41 ) [K]
42 The alphanumeric value of "MATH" (A=1, B=2, etc) [K, PS-M]
Mathematics in 1994 from the University of Illinois in Urbana, Illinois. Since that time she has taught mathematics at the U.S. Air Force Academy (Continued) N Description 69 The largest number in Bingo that stays the same when rotated 180 degrees about its center
- J D Holdener Received Her Ph
J. Holdener received her Ph.D. in Mathematics in 1994 from the
University of Illinois in Urbana, Illinois. Since that time she has taught
mathematics at the U.S. Air Force Academy, Harvard University, Carnegie
(Continued)
N Description
69 The largest number in Bingo that stays the same when rotated 180 degrees about
its center [PS-E]