How to calculate the deviation of points from a curve?

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To calculate the deviation of points from a curve, one effective method is to determine the average distance of the points from the curve, with the root mean square distance being a preferred approach. This method essentially provides the standard deviation of the points in relation to the curve. For a more statistical analysis, conducting a chi-square test can help assess the goodness of fit between the points and the curve. This is particularly useful when dealing with different types of curves, such as quadratic and polar equations. Accurate calculations will enhance the comparison between the various curves modeled.
MelanieBrett
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Hi,
I'm working on some coursework for which I have been modelling a curve to a set of points, and for the final section I am wanting to calculate how close each point is to the curve as a method of comparison between the curves I have calculated. Some of the curves are quadratic, and others are the Cartesian form of some Polar equations. If anyone could offer any help or advice, it would be much appreciated :)
 
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You could try calculating the average distance of each set of points from the curve - perhaps better to look at the root mean square distance. Essentialy the standard deviation of the points from the curve.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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