id: 06560922
dt: j
an: 2016c.00762
au: Choate, Jon
ti: Circles and parabolas in 3-space.
so: Consortium 109, 1-3 (2015).
py: 2015
pu: COMAP (Consortium for Mathematics and Its Applications), Bedford, MA
la: EN
cc: G70 U70
ut: solid geometry; analytic geometry; vector geometry; geometry software;
equations of circles; equations of parabolas; 3D geometry; coordinates;
parameters; parametric equations; geometric constructions;
intersections; 3D curves; visualization
ci:
li:
ab: From the text: This editionâ€™s Geometerâ€™s Corner had its genesis with a
question and a discovery. The question: How do you find the equations
for circles and parabolas in 3-space? The discovery: GeoGebra 5, the
latest GeoGebra update, now has a 3D component that allows you to
define and plot curves and surfaces parametrically using the command
Curve $\langle$\,Expression\,$\rangle$,
$\langle$\,Expression\,$\rangle$, $\langle$\,Expression\,$\rangle$,
$\langle$\,Parameter Variable\,$\rangle$, $\langle$\,Start
Value\,$\rangle$, $\langle$\,End Value\,$\rangle$. Curves can also be
defined constructively using a variety of tools that appear in the MENU
bar. There is an Input Window where one can enter points, vectors, and
implicit definitions of surfaces such as planes. Any time a curve is
defined either by entry or by construction, relevant information about
it appears in the Algebra Window.
rv: