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Parabola Subnormal
The subnormal for a given parabola is constant, and closely related to the focal length.
Parabolic Solar Cooker
Explore the relationship between f-number of a parabolic solar cooker and its sensitivity to change in angle of incoming light
Cubic Spline
Many computer drawing programs use cubic splines to represent arcs. Our diagram shows how a spline can be constructed from 4 control points. We highlight that it is a moving average of two parabolas. These parabolas are exactly the string art parabolas.
watts up
Watt's linkage is used to generate approximate straight line motion in automobile suspensions. Aee how it works. (Yes I'm using an alpha copy of GX version 3.2)
Euclids Elements – Book 1 – Proposition 42
To construct, in a given rectilineal angle, a parallelogram equal to a given triangle. In other words, given angle D and triangle ABC (in blue), construct a parallelogram (in yellow) that has an equal area to triangle ABC.
Tangent Triangle
We show the areas of the triangle formed by joining 3 points on a parabola, and that formed by the tangents to the parabola at those points.
Parabola Property
The triangle containing the normal and tangent at a point on a parabola sits inside a semicircle centered at the parabola's focus.
Squeezing Twisted Savonius Wind Turbine Model
This model demonstrates that the surface of the Twisted Savonius wind turbine's blades are geometrically squeezed as the twist angle is increased and the parametric position is moved up and down the turbine. Learn more about the squeeze. Learn more about the Geometry of the Twisted Savonius Wind Turbine project. Note: the calculated radius in this particular example cannot be accurate because the model is a 2d geometric approximation of the real 3d shape. Accurate calculations are made from the top view model, which is visually more difficult to comprehend. The calculation here still varies accurately as the twist angle is changed and the position is moved up and down the turbine, but it also varies as the rotation is changed (which shouldn't happen).
Tchirnhausen's Cubic
The caustic formed by light projecting perpendicular to the axis of a parabola is called Tchirnhausen's Cubic. What happens when the light projects at some other angle?
