Advanced Knowledge Problem of the Week: Is the vector in the span? [Linear Algebra]

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Solution below.

Problem of the Week 7/25/17 Math inspired Alphametic [puzzle]

Check out this Mathematics inspired Alphametic Problem of the Week
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The two basic rules for solving alphametics are as follows:
Each letter must be represented by a different digit. If the letter is used more than once, it must be represented by the same digit.
Once you substitute digits for all your letters, you must end up with an accurate addition problem.

Solution below.

Episode 6: Area of a Circle [#MathChops]

This problem of determining the area of a circle, or better defined as the area inside of a circle, was a huge dilemma in the field of mathematics. It was not until the mid 200's BC when Archimedes began to anticipate modern calculus and analysis though concepts of infinitesimals and exhaustion, which he used to solve this major challenge of finding the area of a circle.

Archimedes' method of finding the area is described as "squaring the circle", which is trying to find the square that has the same enclosed area as a circle of a given radius. Using this and also using a method where he approximated the area of a circle with other, known shapes such as squares and hexagons, Archimedes was able to determine the area inside of a circle. Take a look at the proof to see how Archimedes came up with the formula we know today:

Advanced Knowledge Problem of the Week: Game of Thrones Committee [Combinatorics]

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Solution below.

Problem of the week 7/18/17 [geometry]

Check out this Problem of the week about Geometry and triangles within a circle. If you're interested in learning more about how you draw circles and what it says about your cultural background, read this article: 

How do you draw a circle? We analyzed 100,000 drawings to show how culture shapes our instincts

Be sure to let us know how you solved it in the comments below or on social media!

Solution below.