Circles Part 1: Similarity Intuition #JulyChallenge2014 5/31

Transformulas

All circles are similar, right?

Okay, maybe it’s not given.  In fact, it needs to be proven.  This proof is yet another that is so easily demonstrated with dynamic math tools (like desmos and geogebra

Circle Similarity with Desmoshttps://www.desmos.com/calculator/vscq2qtp2w

So long as you can move one center onto the other (translate) and dilate one radius to equal the other, similarity is achieved.  This works for every circle.  The perfect proportional balance achieved with circles lays the foundation for most of not all relationships found in them.

Proportional Measures

Similarity gives us a simple system for comparing measures in multiple figures.

2014-07-07_1512

You can even explore this with repetition of congruent triangles:

Dimensional Analysis with Scalehttp://ggbtu.be/m127379

Applications

Below are a couple of applications that push further with exploring the measures of circles, proportionality, and relationships in the measures.

Pizza Pi 

This activity was first inspired by a posting on John Stevens‘ website wyrmath.wordpress.com .  It looks at proportions…

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About Mr-Butler

Math Geek Volleyballer Crochet Crazy

Posted on July 7, 2014, in July14 Challenge, Uncategorized. Bookmark the permalink. Leave a comment.

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