# Browse Classroom Capsules and Notes

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Displaying 991 - 1000 of 1209

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 reversable numbers...
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.

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.