# 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.

Tags: mirror, parabola, caustic

##### 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?

Tags: reflection, solar-cooker

##### 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?

Tags: solar-cooker, reflection

##### 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.

Tags: parabola, catenary

##### Caustic curve as focus of parabola
The red curve is f(x) (for -2≤x≤2).  The blue curve is the terms up to the square term of the Taylor series.  A is the vertex of this parabola, B is its focus. The orange curve is the caustic - envelope of the reflection of vertical rays reflected in a mirror aligned with f(x). Observe that the focus of the parabola traces the caustic.

Tags: caustic, Taylor-series, parabola