Euclid's Muse
your source for INTERACTIVE math apps
Solve First
Apps to accompany my talk \"Solve First - ask questions later\"Tags: solar cookers, parabolas, reflectors, caustics
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Collection Contents:
Simpson Line
Point E lies on the circumcircle of triangle ABC. The projections of E onto the sides of the triangle are colinear. The envelope of such lines forms a deltoid curve. Try dragging E round the circle. Try dragging A B and C. Note that the envelope curve appears to remain equilateral.
Simpson Line and 9 point Circle
The envelope of the Simpson line is seen to be tangent to the 9 point circle and to touch the concentric circle of 3 times the radius.
Parabolic Mirror
Light impinges on a parabolic mirror at angle θ to the vertical. The reflected light concentrates in the region indicated.
Box Solar Cooker
A simple box solar cooker works by reflecting sunlight from its lid into the box. Can you work out a relationship between the angle of the sunlight and the best angle to open the lid? Can you prove it?
Optimal Performance of Box Solar Cooker
The solar concentration ratio of a solar cooker is the ratio of the amount of sunlight concentrated on the target to the size of the target. This model presents the best situation for a given lid angle, and lets you see how much light can be captured at that lid angle. The question is: what lid angle captures the most sunlight?
Parabolic Solar Cooker
Explore the relationship between f-number of a parabolic solar cooker and its sensitivity to change in angle of incoming light
Parabola and catenary
There isn't much difference between a catenary and its approximate parabola. The catenary is the correct model of an ideal chain. But the parabola fits fairly well too.