Formula-Free Geometry. Area and Volume Exact Geometry Easy! Pretty easy! 11 1 1.

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Presentation transcript:

Formula-Free Geometry

Area and Volume

Exact Geometry Easy! Pretty easy!

Inexact Geometry 1 No formula for green area

Random Procedure  Drop a point at any location within the square  The likelihood of a point falling inside the region is determined by the proportion of area that the shaded region fills Uniform Random Occurring with equal probability

Random Points 1

Real Geometry Can we use this for real problems? km YES!

Real Geometry Use a computer to generate MANY random points km

Real Geometry

10 cm

Today’s Challenge

Circle in a Square 2

Simulated Random Points Use the NXT Brick to…

 Find average of five estimates  Find the percent error relative to  Find the ‘standard error’ of samples  Tighter error  better confidence

How Close? Standard Error

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