# Euclid's Muse

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# Search Results for “arcs”

##### Rotating Ellipses with Arcs
Now that you know how two ellipses can rotate such that they are tangent to each other and a third larger ellipse (see this app); the next challenge is to figure out how an arc placed on each ellipse can be constrained (with proportional points along the ellipses) such that each arc always covers half of the ellipse and one endpoint is on the tangent point of the two smaller ellipses.

Tags: Ellipses, conics, puzzler, arcs

By Emily
##### Planet Orbit
Find out how and why Newton invented calculus to solve a proof on planets!

Tags: calculus, integrals, orbits, planets, area, arcs

##### 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).

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

##### 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

##### Geometric Top View Model of the Twisted Savonius Wind Turbine (Interactive)
This app models the top view of the Twisted Savonius Vertical Axis Wind Turbine (VAWT). The various inputs and draggable points allow you to see how the model can trace the blades' surfaces. You can also control the twist angle, radius, and rotation - which makes the whole thing spin! Learn more about the Twisted Savonius Modeling Project here.

Tags: Twisted-Savonius, Top-View, Model, Geometric, Real-World, Circles, Arcs, Loci

By Duncan
##### 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.

Tags: spline, curve, parabola