Why are manhole covers round? – 3.5 minute video
Basic Dice Probability: How Simple is It? – 4 minute video
http://ed.ted.com/lessons/the-last-banana-a-thought-experiment-in-probability-leonardo-barichello
Spirals and Fibonacci in Nature – 6 minutes each
Part 1: https://www.khanacademy.org/math/recreational-math/vi-hart/spirals-fibonacci/v/doodling-in-math-spirals-fibonacci-and-being-a-plant-1-of-3
Part 2: https://www.khanacademy.org/math/recreational-math/vi-hart/spirals-fibonacci/v/doodling-in-math-class-spirals-fibonacci-and-being-a-plant-2-of-3
Part 3: https://www.khanacademy.org/math/recreational-math/vi-hart/spirals-fibonacci/v/doodling-in-math-spirals-fibonacci-and-being-a-plant-part-3-of-3
The Nazi's Enigma Machine and the Mathematics Behind it
http://www.numberphile.com/videos/enigma.html
Learn the flaw which allowed the Allies to break the Nazi Enigma code
http://www.numberphile.com/videos/enigma_flaw.html
Irrational Numbers – History and Mathematics
http://www.numberphile.com/videos/root2.html
PI – What is it exactly? – 4 minute video
http://ed.ted.com/lessons/the-infinite-life-of-pi-reynaldo-lopes
The Science of Origami – 16 minute video
http://www.ted.com/talks/robert_lang_folds_way_new_origami
More to come...