Point Trilateration

Use any three points and their distances from a fourth point to locate the fourth point.

Tags: Geometry, Algebra-2, Trilateration, Location, Applied-Mathematics, Circles

parabola envelope

We use a trick to let the trace "open up" as you drag a point. The trick is this:  an initial point is given parametric location s*t, create a tangent at this point and its envelope as s varies. Now hide the original point and create another point with parameter t, and make it draggable. Dragging the new point changes the value of t and we see a trace from 0 to t.  

Tags: parabola, envelope

Twisted Savonius Wind Turbine Full Geometric Model (without traces/surfaces)

The Twisted Savonius Wind Turbine has promising applications for rooftop usage, but its high cost has kept it unfeasible for widespread adoption. The Twisted Savonius Geometric Modeling project explored the geometric properties of the turbine's shape, and proposed a more efficient method of construction and geometric design as a result. This is the complete side view "3d" model of the turbine. It models an extremely 3-dimensional shape by using ellipses to represent tilted circles. Changing X changes the rotation of the turbine (in operation). Theta represents the twist angle between the top and the bottom of the turbine. T controls the parametric location of the vertical surface - tracing it "fills in" the blade's surface. Learn more about this side view model. Visit the Geometry of the Twisted Savonius Wind Turbine website.

Tags: Twisted-Savonius, Wind-Turbine, Pseudo-3d, Model, Geometric, Real-World, Ellipses, Arcs, Loci