### Random Cool Math Thing #4

Visual Quadratic Reciprocity

#mtt2k
applet
assessment
Chronic Illness
Crohn's
Cylinders
Farey Fractions
First day of class
game
Gradeless
handout
kinesthetic
Learn names
Mini-Quiz
MIT
MOOC
MTEL
Number bases
Ostomy
Pascal's triangle
physics
Polyhedra
Primes
programming
Pythagorean theorem
Random cool math thing
Recursive Equations
sexism
Sierpinski triangle
Sporcle
Study group
syllabus
Tournaments
Transformations
Triangle numbers
Video
Visual proof

The Farey Sequence, \(F_{n}\) is the list of all simplified fractions between \(\dfrac{0}{1}\) and \(\dfrac{1}{1}\) with denominator less than or equal to \(n\). For example,

\( \large F_{5}=\dfrac{0}{1},\dfrac{1}{5},\dfrac{1}{4},\dfrac{1}{3},\dfrac{2}{5},\dfrac{1}{2},\dfrac{3}{5},\dfrac{2}{3},\dfrac{3}{4},\dfrac{4}{5},\dfrac{1}{1}\)

Read more >>

This is a classic problem solving activity that I first saw many years ago in *Mathematics: A Human Endeavor. * The NCTM has a nice applet to test cases one at a time.

Since I like playing with Excel and trying to extend what it can do, I wrote a spreadsheet to represent the problem. The end result is much better than expected — this representation uses a slider to show many cases in a short period of time, and with it I noticed patterns that I never had before (e.g. if you start at (1,0) on a rectangle whose sides have GCD=2, you get a loop that goes through all squares). Read more >>

Sporcle game here. Name all the primes less than 100 in 3 minutes.

buy viagra online

cheap pill viagra

cheap viagra overnight

buy cialis now

buy discount soma

buy viagra internet

buy cialis now

buy viagra with discount

cialis usa

buy viagra las vegas

buy viagra

buy viagra cheaply

buy viagra with discount

buy now cialis

viagra for sale

buy viagra brand

cheap pill viagra

buy cialis online

buy cheap viagra

buy viagra com

buy viagra