The quest for greater unity and truth is achieved by the famous dialectic, positing something (thesis), denying it (antithesis), and combining the two half-truths (synthesis) which contains a greater portion of truth in its complexity.

Do you recall studying for your exams? You probably do. But do you remember how you studied, how you memorized French words or the year of the American civil war? Now, that’s probably harder. As a teenager, Ricardo Lieuw On was packing groceries when he knew what he wanted to study: he wanted to learn about learning. He picked up a study in psychology and learned how to reduce his learning time from 3 hours to 1 hour on the same piece of content. He gained the same knowledge in 200% less time. And specially for TEDxHaarlem, he shares the secret of his technique. This talk was given at a TEDx event using the TED conference format but independently organized by a local community. Learn more at https://www.ted.com/tedx

This is another brillian video from Mathologer. In 2007 a simple beautiful connection Pythagorean triples and the Fibonacci sequence was discovered. This video is about popularising this connection which previously went largely unnoticed. If you want more details go to the video on Mathologer.

Pascal’s Triangle

One of the most interesting Number Patterns is Pascal’s Triangle (named after Blaise Pascal, a famous French Mathematician and Philosopher). …

Diagonals. …

Symmetrical. …

Horizontal Sums. …

Exponents of 11. …

The same thing happens with 11^{6} etc.

Squares. …

Fibonacci Sequence.

The Coefficients of the Binomia Theorem from Pascal’s Triangle

Pascal’s triangle formula is (n+1)C(r) = (n)C(r – 1) + (n)C(r). It means that the number of ways to choose r items out of a total of n + 1 items is the same as adding the number of ways to choose r – 1 items out of a total of n items and the number of ways to choose r items out of a total of n items.

The Fibonacci sequence with Pythagorean triples

The sum of the squares of consecutive Fibonacci numbers is another Fibonacci number. Specifically we have the following right triangle. The hypotenuse will always be irrational because the only Fibonacci numbers that are squares are 1 and 144, and 144 is the 12th Fibonacci number.

Pascal’s triangle is commonly used in probability theory, combinatorics, and algebra. In general, we can use Pascal’s triangle to find the coefficients of binomial expansion, the probability of heads and tails in a coin toss, the probability of certain combinations of things, and so on…

Video

About Mathologer

Enter the world of the Mathologer for really accessible explanations of hard and beautiful math(s). In real life the Mathologer is a math(s) professor at Monash University in Melbourne, Australia and goes by the name of Burkard Polster. These days Marty Ross another math(s) professor, great friend and collaborator for over 20 years also plays a huge role behind the scenes, honing the math(s) and the video scripts with Burkard. And there are Tristan Tillij and Eddie Price who complete the Mathologer team, tirelessly proofreading and critiquing the scripts and providing lots of original ideas. If you like Mathologer, also check out years worth of free original maths resources on Burkard and Marty’s site http://www.qedcat.com.

“The only way to make sense out of change is to plunge into it, move with it, and join the dance.”

Alan Wilson Watts (6 January 1915 – 16 November 1973) was a British-born philosopher, writer, and speaker, best known as an interpreter and populariser of Eastern philosophy for a Western audience. Born in Chislehurst, he moved to the United States in 1938 and began Zen training in New York. Pursuing a career, he attended Seabury-Western Theological Seminary, where he received a master’s degree in theology. Watts became an Episcopal priest in 1945, then left the ministry in 1950 and moved to California, where he joined the faculty of the American Academy of Asian Studies.

Watts gained a large following in the San Francisco Bay Area while working as a volunteer programmer at KPFA, a Pacifica Radio station in Berkeley. Watts wrote more than 25 books and articles on subjects important to Eastern and Western religion, introducing the then-burgeoning youth culture to The Way of Zen (1957), one of the first bestselling books on Buddhism. In Psychotherapy East and West (1961), Watts proposed that Buddhism could be thought of as a form of psychotherapy and not a religion. He also explored human consciousness, in the essay “The New Alchemy” (1958), and in the book The Joyous Cosmology (1962).

Towards the end of his life, he divided his time between a houseboat in Sausalito and a cabin on Mount Tamalpais. His legacy has been kept alive by his son, Mark Watts, and many of his recorded talks and lectures are available on the Internet. According to the critic Erik Davis, his “writings and recorded talks still shimmer with a profound and galvanizing lucidity.