The internet is full of beautiful ideas and inspiring resources. With these at hand, all you need is some motivation to fuel your journey of discovery. From there, you can explore the vast mathematical world, and perhaps even share the fruits of your exploration with friends and family.
As an example, consider the resources of the Global Math Project and Exploding Dots. This wonderful story starts at the very beginning of mathematics - number systems - and is at the heart of this year's Global Math Week.
Another useful resource is our Epsilon Stream. This free app created by our team allows you to watch, play and explore mathematics. Give it a try now.
As we refine the content of Epsilon Stream, we also create monthly Editors' Picks. In this month's edition we have some incredible resources that might just be the inspiration that you need.
Creating The Never-Ending Bloom by SciFri: Artist, designer and inventor, John Edmark, a Stanford educator, discusses his fascination with spiral patterns. Are you surprised that a common theme in much of his work is the golden ratio? Check out this video to learn more, and see some incredible patterns arising in surprising places!
Conditional probability explained visually (Bayes' Theorem) by Art of the Problem: In this video, conditional probability is discussed by considering coin flips where some of the coins are biased, i.e. unfair, or favouring a particular outcome. Brit Cruise investigates using tree diagrams depicting every possible outcome. In some cases, this can be a useful way of understanding a key locomotive of conditional probability problems: Bayes' Theorem.
Can a Chess Piece Explain Markov Chains? by PBS Infinite Series: Do you play chess? Even if you don't, you might enjoy the challenges posed in this video concerning random knight moves. As explained by Kelsey Houston-Edwards, such a process can be modelled by a Markov Chain. Here, the probability of reaching a state in the next step depends the state in the current step. The video is rich with mathematics, however you can enjoy it even if you don't follow every step.
Can We Trust Opinion Polls? by GoldPlatedGoof: Have you ever wondered how statistical facts quoted by journalists are established? For example, "12% of the adult population of the U.S.A. thinks that exercise is not important". To determine this do we ask each and every individual? No, this would be an impossible task! How is it, then, that we can make such strong statements? This video explores the world of statistical sampling as well as some amazing consequences of the Central Limit Theorem.
These Shapes are the Same by Tipping Point Math: Is it obvious that if we have two polygons of the same area, one can be chopped up into triangles and rearranged to form the other? Watch this beautiful video explaining dissections. It is a very deep result that can have implications in many other areas of mathematics.
Chaos Game | Fractals emerging from chaos | Computer simulation | by Think Twice: On applying a small set of simple rules for replicating points within certain polygons, we see amazing phenomena - fractal patterns appear! Usually in mathematics, chaos refers to deterministic systems (i.e. not random ones) with certain technical features (like sensitivity to initial conditions). In this video, the element of randomness imposed on the set of rules results in a system which is not really chaotic in this sense; nevertheless the results are stunning! Do you want to improve your programming skills? If so, this would be a perfect opportunity to try replicating some of these experiments yourself.
HARD Geometry Puzzle In The Simpsons by MindYourDecisions: In this cool, fast paced video, Presh Talwalkar tells us about some of the curious mathematics problems that appear in the 26th season finale of The Simpsons. One outstanding problem is a simply stated geometry puzzle. It isn't deep, but it certainly isn't easy! Can you solve it?
We hope you enjoyed our selection. Let us know what you think. Remember, you can also get these videos on Epsilon Stream. If you like what you see, be sure to register with us for content updates, and follow us on Twitter. Also stay tuned for events associated with the 2018 Global Math Week.