# Browse Classroom Capsules and Notes

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Displaying 991 - 1000 of 1212

The author displays an example of a domain where factorization is not unique.

The author provides a visual solution for the alternating sum of an even number of triangular numbers.

This paper seeks the minimal structure needed to mimic Gödel's formal system with regard to self-referring sentences, incompleteness, the futility of striving for completeness, and...

The number 1089 has the curious property that when one reverses its digits, an integer multiple of itself is obtained. The author gives a structure theorem for certain sets of reversible...

The author gives a rule which approximates the integral representing the Gini coefficient, and which is exact for 5th degree poynomials.

The paper gives a short proof that for any $n$ x $n$ matrices $A$ and $C$ over a field of scalars, $AC = I$ if and only if $CA = I$. The proof relies on familiarity with...

The article answers negatively the question, “Is there a (non-trivial) linear transformation $T$ from $P_n$, the vector space of all polynomials of degree at most $n$, to $P_n$...

The author presents a new elementary geometric result involving cyclic polygons and product relations, accessible to undergraduates.

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.