College Mathematics Journal Contents—November 2016

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