Some Trigonometric Identities
Advanced Knowledge Problem of the Week: Is the vector in the span? [Linear Algebra]
Be sure to let us know how you solved this in the comments below or on social media! Solution below. Solution Video
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Episode 5: Königsberg Bridge Problem (Seven Bridges) [#MathChops]
The advent of graph theory, from the mind of Leonhard Euler, came from a long-standing problem for the people of Königsberg. The problem was that no couple had a long and happy marriage, if they were married in Königsberg. As tradition dictated, a newlywed couple had one chance to travel across Königsberg’s four land masses using each of the seven bridges once and only once. If the two lovers could complete this seemingly simple task, their marriage would be long and happy. Years went by and nobody could complete to task, until Euler constructed a mathematical object that broke the curse of Königsberg… a graph! Watch the proof proposed by Euler below to learn how mathematical abstraction created a whole new field of math, which is now regarded as an important predecessor to topology. Euler’s invention itself is remarkable, but the implications to mathematical philosophy reveals something very deep in the heart of mathematics. Namely, the art of abstraction to gain a better understandin...
Advanced Knowledge Problem of the Week: 7-6-17 [calculus]
Be sure to let us know how you did in the comments below or on social media! This week's problem comes from our textbook, Worldwide Multivariable Calculus , so feel free to check it out or any other affordable texts we offer. Enjoy this problem and try to find its relation to July 4th! Solution below. Solution Video
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