In geometry, Playfair's axiom is an axiom that can be used instead of the fifth postulate of Euclid (the parallel postulate): In a plane, given a line and a point not on it, at most one line parallel to the given line can be drawn through the point. It is equivalent to Euclid's parallel postulate in the context of Euclidean geometry and was named after the Scottish mathematician John Playfair. The "at most" clause is all that is needed since it can be proved from the remaining axioms that at least one parallel line exists. The statement is often written with the phrase, "there is one and only one parallel". In Euclid's Elements, two lines are said to be parallel if they never meet and other characterizations of parallel lines are not used. This axiom is used not only in Euclidean geometry but also in the broader study of affine geometry where the concept of parallelism is central. In the affine geometry setting, the stronger form of Playfair's axiom (where "at most one" is replaced by "one and only one") is needed since the axioms of neutral geometry are not present to provide a proof of existence. Playfair's version of the axiom has become so popular that it is often referred to as Euclid's parallel axiom, even though it was not Euclid's version of the axiom. (Wikipedia).
We (could) live on a 4D Pringle (Non-Euclidean Geometry and the shape of the Universe)
Everything we were taught in geometry falls apart if our universe is curved. This video is a friendly introduction to non-Euclidean geometry and how cosmologists used the Cosmic Microwave Background to calculate the curvature of our universe. See Part Two of the shape of the universe duo
From playlist Summer of Math Exposition 2 videos
Simplify a rational expression by using properties of exponents
👉 Learn how to simplify expressions using the quotient rule of exponents. The quotient rule of exponents states that the quotient of powers with a common base is equivalent to the power with the common base and an exponent which is the difference of the exponents of the term in the numerat
From playlist Simplify Using the Rules of Exponents | Quotient Rule
Simplify rational expression using the rules of exponents
👉 Learn how to simplify expressions using the quotient rule of exponents. The quotient rule of exponents states that the quotient of powers with a common base is equivalent to the power with the common base and an exponent which is the difference of the exponents of the term in the numerat
From playlist Simplify Using the Rules of Exponents | Quotient Rule
Simplify an expression by applying quotient rule of exponents
👉 Learn how to simplify expressions using the quotient rule of exponents. The quotient rule of exponents states that the quotient of powers with a common base is equivalent to the power with the common base and an exponent which is the difference of the exponents of the term in the numerat
From playlist Simplify Using the Rules of Exponents | Quotient Rule
How to make Data Visual: Extending Tufte and Playfair
Animation on how apply modern techniques to William Playfair's graphs. Also extends the ideas of Edward Tufte. Like us on: http://www.facebook.com/PartyMoreStudyLess David Longstreet Professor of the Universe Professor of the Universe: David Longstreet http://www.linkedin.com/in/david
From playlist Visualization of Data
Learn the basics for simplifying an expression using the rules of exponents
👉 Learn how to simplify expressions using the quotient rule of exponents. The quotient rule of exponents states that the quotient of powers with a common base is equivalent to the power with the common base and an exponent which is the difference of the exponents of the term in the numerat
From playlist Simplify Using the Rules of Exponents | Quotient Rule
DEFCON 18: Tales from the Crypt 2/4
Speaker: G. Mark Hardy Learn how to crack crypto contests like a pro. The speaker has awarded half a dozen free round-trip plane tickets to previous contest winners. Maybe you'll be next. From the daily newspaper puzzle to badge contests to codes that keep the National Security Agency a
From playlist DEFCON 18-1
Simplifying a rational expression using the property of exponents
👉 Learn how to simplify expressions using the quotient rule of exponents. The quotient rule of exponents states that the quotient of powers with a common base is equivalent to the power with the common base and an exponent which is the difference of the exponents of the term in the numerat
From playlist Simplify Using the Rules of Exponents | Quotient Rule
Simplify a rational expression with two variables
👉 Learn how to simplify expressions using the quotient rule of exponents. The quotient rule of exponents states that the quotient of powers with a common base is equivalent to the power with the common base and an exponent which is the difference of the exponents of the term in the numerat
From playlist Simplify Using the Rules of Exponents | Quotient Rule
How to simplify an expression using rules of exponents
👉 Learn how to simplify expressions using the quotient rule of exponents. The quotient rule of exponents states that the quotient of powers with a common base is equivalent to the power with the common base and an exponent which is the difference of the exponents of the term in the numerat
From playlist Simplify Using the Rules of Exponents | Quotient Rule
Hyperbolic Knot Theory (Lecture - 1) by Abhijit Champanerkar
PROGRAM KNOTS THROUGH WEB (ONLINE) ORGANIZERS: Rama Mishra, Madeti Prabhakar, and Mahender Singh DATE & TIME: 24 August 2020 to 28 August 2020 VENUE: Online Due to the ongoing COVID-19 pandemic, the original program has been canceled. However, the meeting will be conducted through onl
From playlist Knots Through Web (Online)
Colin Beveridge - An Old-Timey Cipher - G4G13 Apr 2018
Or, how I failed to solve a puzzle (and you can too!).
From playlist G4G13 Videos
King George VI - 25th October 1945
King George VI and Queen Elizabeth in 1945 visited Imperial College to commemorate the centenary of the Royal College of Science, oldest forerunner to Imperial. King George said: "You students here assembled - men and women who soon will be going out from the Imperial College to your work
From playlist King George VI - Speeches and Broadcasts
How to simplify an expression use the rules of exponents
👉 Learn how to simplify expressions using the quotient rule of exponents. The quotient rule of exponents states that the quotient of powers with a common base is equivalent to the power with the common base and an exponent which is the difference of the exponents of the term in the numerat
From playlist Simplify Using the Rules of Exponents | Quotient Rule
Kim Rees keynote Strata Conference London 2012 "The Dirty Truth about Data Literacy"
Kim Rees is a founding partner of Periscopic: http://www.periscopic.com, an award-winning information visualization firm. Their work has been featured in the MoMA as well as several online and print publications, including CommArts' Interactive Annual, The Information Design Sourcebook, Pr
From playlist Strata in London 2012
Ruby Conf 2011 Better Than ROT13 by Bradley Grzesiak
We use encryption every day, from SSL to SSH to passing notes to your crush during Social Studies class. But how does it actually work? I'll avoid most of the math but cover the concepts of both symmetric and asymmetric encryption, including hashing and signing. I'll also show how to use O
From playlist Ruby Conference 2011
DEFCON 18: Tales from the Crypt 1/4
Speaker: G. Mark Hardy Learn how to crack crypto contests like a pro. The speaker has awarded half a dozen free round-trip plane tickets to previous contest winners. Maybe you'll be next. From the daily newspaper puzzle to badge contests to codes that keep the National Security Agency a
From playlist DEFCON 18-1
Simplifying a monomial using the rules of exponents
👉 Learn how to simplify expressions using the quotient rule of exponents. The quotient rule of exponents states that the quotient of powers with a common base is equivalent to the power with the common base and an exponent which is the difference of the exponents of the term in the numerat
From playlist Simplify Using the Rules of Exponents | Quotient Rule
How to simplify dividing two monomials Math help
👉 Learn how to simplify expressions using the quotient rule of exponents. The quotient rule of exponents states that the quotient of powers with a common base is equivalent to the power with the common base and an exponent which is the difference of the exponents of the term in the numerat
From playlist Simplify Using the Rules of Exponents | Quotient Rule
History of Science and Technology Q&A (September 21, 2022)
Stephen Wolfram hosts a live and unscripted Ask Me Anything about the history of science and technology for all ages. Find the playlist of Q&A's here: https://wolfr.am/youtube-sw-qa Originally livestreamed at: https://twitch.tv/stephen_wolfram If you missed the original livestream of thi
From playlist Stephen Wolfram Ask Me Anything About Science & Technology