A Preview of What's Coming to GXWeb
We're putting the finishing touches on a meaningful expansion to GXWeb. Conic support, ellipses, hyperbolas, and parabolas, is on its way, enabling users to construct, manipulate, and explore a whole new class of geometric features inside the interactive workspace they already know.
Why conics matter
As our President, Phil Todd, notes, our Conic sections have been studied by mathematicians since Archimedes' time. An ellipse is the shape you get when you take a circle and stretch it. We're all familiar with the construction of an ellipse from two pins and a piece of string, but there are dozens of other ways of drawing this curve.
Because of the stretched-circle property, the ellipse is the shape of narrow beams of sunlight through the leaf canopy and projected on the ground. It is the apparent shape of a circle on a piece of paper when viewed from an angle. The focal property of an ellipse guarantees that any sound projected from one focus (the place your pin goes in the pin-and-string construction) reflects to the other. The Whispering Chamber in the US Capitol is an example of this property.
The parabola can be thought of as an ellipse with one focus dragged off to infinity. So, it creates an echo chamber with one participant way out in space. This is why radio telescopes are parabolic in shape.
A line through one focus, reflected in the tangent, passes through the other focus.
See conics in practice
A preview of what's coming. The four examples below are drawn from our book, 101 Conic Sections Examples Using Geometry Expressions, which we're giving away as part of the launch.
Ellipse
Parabola Subnormal
Hyperbola
Ellipse Hyperbola
Generating conics by description in GenGX
Conic support in GXWeb also opens new possibilities in GenerativeGX (“GenGX”). With conics in the underlying engine, GenGX can produce figures that include ellipses, hyperbolas, and parabolas from a simple description. Type or speak what you want, a parabolic trajectory, an elliptical orbit, a hyperbolic curve, and watch a mathematically correct, interactive diagram appear.
What to expect
Sign up to be notified when GXWeb conics goes live, and you'll be among the first to know.
Get notified about the GXWeb conics launch at https://geometryexpressions.com/gxweb/newsletter/