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For questions in Mathematics Education as a scientific discipline. For more hands-on questions on teaching Mathematics, please use the tag teaching. There is also a Stack Exchange community http://matheducators.stackexchange.com/

16 votes
3 answers
2k views

Solving a modified birthday problem at a glance

Modified Birthday Problem: a bunch of people line up, and the winner is the first person who shares their birthday with someone lined up ahead of them. What position in the line is optimal? Three (sim …
Benjamin Dickman's user avatar
9 votes
1 answer
631 views

De-Nesting Absolute Value Function into Linear Combination of Absolute Value Functions

Context: In formulating problems for secondary school mathematics teachers (and students) about absolute value functions, which we define as functions $\mathbb{R} \rightarrow \mathbb{R}$ that send $x …
Benjamin Dickman's user avatar
12 votes
4 answers
2k views

Seeking a Geometric Proof of a Generalized Alternating Series' Convergence

Let $z \in \mathbb{C} \backslash \lbrace 1 \rbrace$ with $|z| = 1$. We consider the following infinite series, which necessarily converges: $$S(z) := \sum_{n = 1}^{\infty}\frac{z^n}{n}$$ Note that $S …
Benjamin Dickman's user avatar
60 votes
1 answer
6k views

Probability that a stick randomly broken in five places can form a tetrahedron

Edit (June 2015): Addressing this problem is a brief project report from the Illinois Geometry Lab (University of Illinois at Urbana-Champaign), dated May 2015, that appears here along with a foot-not …
Benjamin Dickman's user avatar