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One deck. Fifty-two cards. How many arrangements? Let's put it this way: Any time you pick up a well shuffled deck, you are almost certainly holding an arrangement of cards that has never before existed and might not exist again. Yannay Khaikin explains how factorials allow us to pinpoint the exact (very large) number of permutations in a standard deck of cards.
An algorithm is a method of solving problems both big and small. Though computers run algorithms constantly, humans can also solve problems with algorithms. David J. Malan explains how algorithms can be used in seemingly simple situations and also complex ones.
Why are most manhole covers round? Sure it makes them easy to roll, and slide into place in any alignment. But there’s another, more compelling reason, involving a peculiar geometric property of circles and other shapes. Marc Chamberland explains curves of constant width and Barbier’s theorem.
The entire field of mathematics summarised in a single map! This shows how pure mathematics and applied mathematics relate to each other and all of the sub-topics they are made from.
2017 • Math
Mathematical formulas can be found in the arrangement of seeds on a sunflower, the structure of the spirals in the shells of certain marine animals, and the distribution of leaves around a plant stem. These formulas recur in nature from snowflakes to the stripes on a zebra.
2017 • Nature's Mathematics • Math