Inspired by Vi Hart’s most recent doodling video “Triangle Party!”, this week’s post is all about triangles.

Connie Liu

One of the most amazing things about mathematics is that there are always new discoveries to be made about even the simplest of objects–even triangles! Check out this article about Connie Liu, a Hawaiian teenager who just last year discovered some new formulas that relate special points of triangles to each other. Connie has found some new, simple, and interesting ways of describing the triangle inequality – just by sticking with her questions and digging into a particular part of mathematics a little deeper than anyone had before.

Next up, here are some visual perspectives on Pascal’s triangle. Even folks who are well acquainted with this numerical cascade are likely to find something new to see in these blog posts by Tao Wang. Tao is a math and computer teacher in NYC. My favorite visualization is the video that depicts the entries of Pascal’s triangle as blocks that are as tall as their numerical value.

Hat tip to Patrick Honner, a math teacher from Brooklyn, for the Pascal’s triangle visualizations. Patrick writes a sweet mathematical blog, including a running series of photographs about the math that he sees in the world. Check out his posts about which of these isosceles triangles is “more equilateral.”

Zooming in on the corner of a Koch snowflake.

Finally, Vi mentions and doodles a Koch snowflake in her video. This seems timely, what with snowfalls likely just around the corner. Here are some great images of generalizations of the Koch snowflake by Phil Keenan that he made using computers.

Wow, what a great crop of other blogs for you to explore!

Thanks for the mention!

There are more interesting things going on with triangles on my blog recently: http://mathlaoshi.com/2011/12/15/the-tangent-identity-in-geogebra/

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