# Browse Classroom Capsules and Notes

You can filter the list below by selecting a subject category from the drop-down list below, for example by selecting 'One-Variable Calculus'. Then click the 'APPLY' button directly, or select a subcategory to further refine your results.

Displaying 1001 - 1010 of 1214

It is known that every positive odd integer can be expressed in the form $$x^2 + y^2 + 2z^2$$ for some integers $$x$$, $$y$$ and $$z$$. The authors discuss the non-existence of certain...

A visual binomial coefficient identity is presented.

A visual decomposition of a triangle is given.
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...

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.

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

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...

A Fundamental-like Theorem of Algebra for exponential functions is discussed and proved.
The author discusses the question of when to add milk to coffee in order to maximize cooling.
The author discusses the distribution of solutions to a polynomial congruence as the modulus varies.