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Fibonacci & Pythagoras Help save a beautiful discovery from oblivion

Pythagorean Triples

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 116 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.

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Alan Watts

Alan Watts
Alan Watts

“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.

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3 things I learned while my plane crashed

Ric Elias

Ric Elias had a front-row seat on Flight 1549, the plane that crash-landed in the Hudson River in New York in January 2009. What went through his mind as the doomed plane went down? At TED, he tells his story publicly for the first time.

Ric Elias is the CEO and cofounder of Red Ventures, a portfolio of fast-growing digital businesses.

Why you should listen

Ric Elias was given the gift of a miracle: to face near-certain death, and then to come back and live differently.

Video 4m 45s

Ric Elias – Ted Talks

A native of Puerto Rico, Elias attended Boston College and Harvard Business School before starting his career as part of GE’s Financial Management program. He cofounded Red Ventures in 2000, just months before the dot-com bubble burst. The company weathered the storm; by 2007 it was ranked fourth on the Inc. 500 list, and in 2015 the company was valuated at more than $1 billion. Elias has cultivated an award-winning company culture, ranking as a “Best Place to Work” in Charlotte, North Carolina, for ten years in a row.

Elias’s leadership style and personal life are deeply influenced by his experience as a survivor of Flight 1549, also known as the “Miracle on the Hudson.” He is devoted to using his platform to “leave the woodpile higher than he found it” — spinning out multiple nonprofits from Red Ventures over the years, all of which are aimed at creating educational opportunity and economic mobility for under-served groups. In 2018, Elias launched Forward787, a social enterprise committed to raising and deploying $100 million to build businesses in Puerto Rico that compete with the world’s top companies. In 2019, he launched a podcast, 3 Things with Ric Elias, as a continuation of the learning journey he shared on the TED stage.