MathDB

4

Part of 2007 Stanford Mathematics Tournament

Problems(3)

SMT 2007 Team #4

Source:

6/30/2012
What is the area of the smallest triangle with all side lengths rational and all vertices lattice points?
geometry
String of Tangents

Source:

3/15/2010
Evaluate (tan⁡10∘)(tan⁡20∘)(tan⁡30∘)(tan⁡40∘)(tan⁡50∘)(tan⁡60∘)(tan⁡70∘)(tan⁡80∘) (\tan 10^\circ)(\tan 20^\circ)(\tan 30^\circ)(\tan 40^\circ)(\tan 50^\circ)(\tan 60^\circ)(\tan 70^\circ)(\tan 80^\circ).
trigonometry
SMT 2007 Algebra #4

Source:

6/27/2012
How many positive integers nn, with n≤2007n\le 2007, yield a solution for xx (where xx is real) in the equation ⌊x⌋+⌊2x⌋+⌊3x⌋=n\lfloor x \rfloor+\lfloor 2x\rfloor+\lfloor 3x\rfloor=n?
floor function