# Search Results for “angle”

##### Chord Angle Theorem

The chord angle theorem states that in an inscribed triangle (ABC) where A is the center of the circle and BC is a chord, and BDC is an inscribed triangle on the same chord, angle BDC must equal one half of angle BAC. Try changing the angle and moving point D and observe the theorem’s truth. Note: the measure of angle BDC is being constantly recalculated as point D is dragged, but it doesn't change because of this theorem.##### Euclids Elements - Book 1 - Proposition 45

Creating a parallelogram equal to a given quadrilateral with a given angle.##### Basic Unit Circle

This very basic representation of the unit circle displays the unit circle with an input for the standard angle θ in degrees (which controls the angle between the hypotenuse and the x axis). The outputs represent the other two sides of the triangle and give their lengths through decimals. A good investigation for geometry students is to have them test out different angles here, then compare the results to those testing the angles with sine and cosine on their calculators. This allows them to visualize the unit circle in a precise diagram rather than simply running inputs and outputs on their calculators.##### 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).*

##### 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.##### 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?##### 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.