The last issue of volume 47 features an exploration of the sine of one degree. This simple sounding question leads to a romp through trigonometry, algebra, and complex analysis, leading us to the most complicated formula ever typeset for an MAA journal!
Two pairs of articles also merit special mention. The Pythagorean theorem, that perennially popular topic, is given a new long proof. And the authorship of the proof commonly attributed to Leonardo da Vinci is called into question.
Finally, paired reviews consider new releases involving both Ken Ono and Srinivasa Ramanujan. An autobiography written with the late Amir Aczel focuses on the impact of the Indian mathematician on Ono's mathematical and personal life. And Ono was heavily involved in a recent film on Ramanujan's life starring Dev Patel and Jeremy Irons. —Brian Hopkins
Vol. 47, No. 5, pp. 321-400
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ARTICLES
The Sine of a Single Degree
p. 322.
Travis Kowalski
Ostensibly a derivation of an algebraically exact formula for the value of te sine of 1 degree, we present this calculation as a "historical romp" looking at the problem through the tools of geometry, then algebra, and finally complex analysis. Each one of these approaches gets the reader nearer to the correct value, but also serves to frame a vignette of surprising or beautiful mathematics.
To purchase from JSTOR: http://www.jstor.org/stable/10.4169/college.math.j.47.5.322
Form
p. 333.
Sarah Blake
To purchase from JSTOR: http://www.jstor.org/stable/10.4169/college.math.j.47.5.333
When You Wander off on a Tangent, Where Do You End Up?
p. 334.
Melissa Mark and Michael Schramm
We consider the set consisting of the union of all tangent lines to continuously differentiable functions. In particular, the complement of this set has a predictable structure.
To purchase from JSTOR: http://www.jstor.org/stable/10.4169/college.math.j.47.5.334
Do the Twist! (on Polygon-Base Boxes)
p. 340.
sarah-marie belcastro and Tamara Veenstra
Folding polygon-base twist boxes is fun, useful, and an appropriate enrichment activity for math classes, math clubs, and individual mathematical experimentation alike. This article is a guide for the use of, and mathematics within, a set of discovery-based activities about the mathematics of folding polygon-base twist boxes. The mathematics rangers from plane geometry through trigonometry to calculus and contains at least one surprise.
To purchase from JSTOR: http://www.jstor.org/stable/10.4169/college.math.j.47.5.340
Proof Without Words: The Lateral Surface Area of a Conical Frustum
p. 346.
Miyeon Kwon
We present visual proofs for the later surface area of a frustum of a right circular cone by relating the unwrapped surface to a rectangle.
To purchase from JSTOR: http://www.jstor.org/stable/10.4169/college.math.j.47.5.346
Winning a Pool is Harder than You Thought
p. 347.
John P. Bonomo
This article addresses the question of whether or not it is possible to know if you are mathematically eliminated from a type of betting pool known as a confidence pool. We show that this problem falls in the category of NP-complete problems, meaning that there is almost surely no quick method to determine the answer.
To purchase from JSTOR: http://www.jstor.org/stable/10.4169/college.math.j.47.5.347
Proof Without Words: A Right Triangle Identity
p. 355.
Roger B. Nelsen
We use a figure to relate the semiperimeter, inradius, and circumradius of a right triangle.
To purchase from JSTOR: http://www.jstor.org/stable/10.4169/college.math.j.47.5.355
A New and Rather Long Proof of the Pythagorean Theorem by Way of a Proposition on Isosceles Triangles
p. 356.
Kaushik Basu
This paper provides a new, long proof of the Pythagorean theorem. The two lemmas used should be of some intrinsic interest, especially one on isosceles triangles.
To purchase from JSTOR: http://www.jstor.org/stable/10.4169/college.math.j.47.5.356
Leonardo da Vinci's Proof of the Pythagorean Theorem
p. 361.
Franz Lemmermeyer
We present evidence suggesting that the proof of the Pythagorean theorem widely attributed to Leonardo da Vinci is actually due to J. T. Mayer in the late 18th century.
To purchase from JSTOR: http://www.jstor.org/stable/10.4169/college.math.j.47.5.361
Classroom Capsules
Trigonometric Derivatives Made Easy
p. 365.
Piotr Josevich
We give geometric proofs of the basic trigonometric derivative formulas, avoiding the trigonometric limit formulas required in the usual limit definitions.
To purchase from JSTOR: http://www.jstor.org/stable/10.4169/college.math.j.47.5.365
Algebraic Characterization of Two Independent Events
p. 367.
Armen Bagdasaryan and Josep Batle
In this short note, we present an equivalent statement for two independent events and inequalities related to their probabilities.
To purchase from JSTOR: http://www.jstor.org/stable/10.4169/college.math.j.47.5.367
Problems and Solutions
p. 369.
To purchase from JSTOR: http://www.jstor.org/stable/10.4169/college.math.j.47.5.369
Book Review
Review: My Search for Ramanujan: How I Learned to Count By Ken Ono and Amir D. Aczel
p. 375.
Reviewed by: Brian Hopkins
To purchase from JSTOR: http://www.jstor.org/stable/10.4169/college.math.j.47.5.375
Film Review
Review: The Man Who Knew Infinity Directed by Matthew Brown
p. 381.
Reviewed by: Jennifer Wilson
To purchase from JSTOR: http://www.jstor.org/stable/10.4169/college.math.j.47.5.381
Media Highlights
p. 386.
To purchase from JSTOR: http://www.jstor.org/stable/10.4169/college.math.j.47.5.386
George Pólya Awards for 2016
p. 394.
To purchase from JSTOR: http://www.jstor.org/stable/10.4169/college.math.j.47.5.394