Student Discoveries
I have been fortunate to work with students and teachers who are excited about original creative work in mathematics.
Here is a list of recent articles that have been published as a result of student work.
PIT YOUR WITS AGAINST YOUNG MINDS
Appeared in the Mathematical Intelligencer, 29 (3), Summer 2007, pp: 55-59.
www.ucm.es/BUCM/compludoc/W/10710/03436993_1.htm
This article surveys a series of results and discoveries made by students over the past few years. If you would like a pdf copy of the article (in case the above website does not link to the article itself, please send an e-mail to mathinstitute@stmarksschool.org.)
AN ILLUMINATING APPROACH TO THE MOBIUS FUNCTION
Appeared in FOCUS, 27 no. 3 (2007), 16-17.
www.maa.org/pubs/march07web.pdf
This article represents the result of the Spring 2007 Math Institute research class.
MATH CIRCLES AND OLYMPIADS
Appeared in Notices, 53 No. 2 (2006), 200-205
www.ams.org/notices/200602/fea-tanton.pdf
This article chiefly speaks of issues relevant to mathematics education but does make some comment towards student results.
PROOF WITHOUT WORDS
Co-authored with former St. Mark's student Nicholas Roumas, this piece proves – without words – that is impossible to draw an equilateral triangle on a square array of dots. It is soon to appear in the College Mathematics Journal.
YOUNG STUDENTS APPROACH INTEGER TRIANGLES
Co-authored with students of the Boston Math Circle FOCUS, 22 no. 5 (2002), 4-6.
www.maa.org/features/integertriangles.pdf
Students prove – in a wonderfully innovative and elegant way – that there are (N^2)/48 (rounded to the nearest integer) distinct triangles with integer side lengths and of perimeter N if N is even, and (N+3)^2/48 such triangles if N is odd.
A DOZEN HAT PROBLEMS
Co-authored with Dr. Ezra Brown and with special assistance from student Alex Smith of St. Mark's School! (Submitted to MATH HORIZONS.)
PROOF WITHOUT WORDS
College Mathematics Journal, 2006
Co-authored with participants of the summer 2005 geometry course for teachers, this piece proves the classic result that the in-radius of an equilateral triangle is one third the altitude of the triangle.
A NEW INTEGER SEQUENCE
St. Mark's student Alex Bishop discovered a new integer sequence that was accepted onto Neil Sloane's Integer Sequence list: