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David Radcliffe
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483 followers
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I wrote a Python script to find all ways to cover an 8x8 square, corners removed, using all 12 pentominoes. I found 493 solutions up to rotation and reflection.
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Matt Enlow asked an interesting question: What is the largest subset of the 25 lattice points in a 5x5 grid such that no two triangles whose vertices come from the subset are congruent? It turns out that the answer is 7, and there are 28 different ways to choose these 7 points, up to symmetry. (Now, what is the size of the largest subset of the NxN grid with this property?)
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Let ABCD be a convex quadrilateral. A smaller quadrilateral PQRS is formed inside ABCD by joining each vertex to the midpoint of a non-adjacent side: A to the midpoint of BC, B to the midpoint of CD, C to the midpoint of DA, and D to the midpoint of AB. Then the area of PQRS can range between 1/5 and 1/6 of the area of ABCD. I wrote up a proof sketch on Stack Exchange. Was this result known previously? http://math.stackexchange.com/questions/1925901/quadrilateral-formed-by-connecting-the-vertices-of-a-convex-quadrilateral-to-mid?stw=2
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I presented a talk tonight at the Twin Cities R User Group. The talk showed how to use R to scrape data from a website, look up latitudes and longitudes, and display it on an interactive map, using Walmart store closings as an example. I hope that it is useful for other people who are creating interactive maps.

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I thought I'd share my results on a fun math problem. Suppose that an infection spreads among the squares of a checkerboard in such a manner that a square with three infected neighbors becomes infected itself. What is the smallest number of squares that must be infected initially for the infection to spread to the entire board?

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The Franklin graph shows the connections between the 12 different ways to express a+b+c. Each edge represents an application of the commutative or transitive law. Was this known previously?
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