Euclid's Muse

your source for INTERACTIVE math apps

Search Results for “Parabola”

By Phil Todd
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.


By Phil Todd
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.

Tags: parabola, Archimedes

By Phil Todd
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?

Tags: Parabola, caustic

By Duncan
String Art
Examine the parabola created in a simple string art figure.  

Tags: parabola, conic

By Phil Todd
Projectile High Point
Press the play button to fire a projectile in the direction of the arrow. Move the arrow and try again. Notice the high points of the trajectory lie on an ellipse.  If the initial velocity of the projectile is v, and gravity is g, what is the equation of the ellipse?

Tags: projectile, parabola, ellipse, physics

By Phil Todd
Parabolic Solar Cooker
Explore the relationship between f-number of a parabolic solar cooker and its sensitivity to change in angle of incoming light  

Tags: parabola, solar-cooker, reflection

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

By Phil Todd
Hyperbola Polar Line
The polar line is the locus of the intersections of tangent lines at the ends of chords of teh parabola through a fixed point. Turns out to be conceptually important - not just a curiosity.

Tags: polar, conic, hyperbola

© Saltire Software Terms and Conditions