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Browse Classroom Capsules and Notes

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Displaying 941 - 950 of 1211

Museum Exhibits for the Conics
Hands-on construction of conical curves
Proof without Words: Gabriel's Staircase
A geometric proof of the sum of an infinite series. Gabriel's Staircase is \(\sum_{k=1}^{\infty} k r^k\).
The Birthday Problem Revisited
The author derives approximations for the probability arising in birthday-type problems without using calculus.
Proof without Words: Geometric Series
A geometric proof of the sum of geometric series
People Who Know People
Elementary proofs and connections between two party guest problems using graph theory techniques
The Importance of a Game

Probabilistic analysis of the importance of a game in a series of games in a competition

Matrix Representation of Finite Fields
The author uses matrices to represent finite fields in order to make both addition and multiplication obvious.
Proof without Words: A Triangular Identity
A geometric demonstration of a recursive identity for triangular numbers
A New (?) Test for Convergence of Series

A new test for the convergence of infinite series with a proof

Proof without Words: The Volume of a Hemisphere via Cavalieri's Principle
The formula for the volume of a sphere is derived using Cavalieri's Principle.

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