Browse Classroom Capsules and Notes

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Proof Without Words: Every Triangle Can Be Subdivided into Six Isosceles Triangles

A visual decomposition of a triangle is given.

Fitting One Right Triangle in Another

The authors answer the question in the title of the paper. This result constitutes part of the output of an undergraduate summer research project by the second author under the supervision of...

The Classification of Similarities: A New Approach

In plane geometry, if a similarity is not an isometry, it is either a dilative rotation or a dilative reflection. A new proof is given based on Apollonius circles.

On Candido's Identity

The authors discuss the existence of functions from the nonnegative reals to the nonnegative reals that satisfy the functional equation underlying Candido`s identity.

Monotonic Convergence to \(e\) via the Arithmetic-Geometric Mean

Hansheng Yang and Heng Yang used the arithmetic-geometric mean inequality to prove that the sequence \([1+1/n]^n\) is monotonic increasing converging to \(e\) whereas \([1+1/n]^{n+1}\) is...

The Lost Cousin of the Fundamental Theorem of Algebra

A Fundamental-like Theorem of Algebra for exponential functions is discussed and proved.

Not Mixing Is Just as Cool

The author discusses the question of when to add milk to coffee in order to maximize cooling.

Polynomial Congruences and Density

The author discusses the distribution of solutions to a polynomial congruence as the modulus varies.

A Curious Way to Test for Primes

Primality testing via repeated differentiation of certain functions is the topic of this paper.

Shanille Practices More

A solution to a probabilistic Putnam Exam Problem is presented.