soft question - What is the real life use of hyperbola?
2013年4月12日 · Applications of hyperbola. Dulles Airport, designed by Eero Saarinen, has a roof in the shape of a hyperbolic paraboloid. The hyperbolic paraboloid is a three-dimensional surface that is a hyperbola in one cross-section, and a parabola in another cross section. This is a Gear Transmission. Greatest application of a pair of hyperbola gears:
How we can differentiate between the shapes of a parabola and a …
2019年12月1日 · $\begingroup$ The hyperbola's plane doesn't have to be parallel to the cone axis, it just has to be "steeper" than the parabola's plane ... that is, it must meet both parts of a double-napped cone (only one of which is indicated in your figure), thereby creating the two branches of the conic. $\endgroup$
analytic geometry - Hyperbolic lens shape and aspheric surfaces ...
2022年11月10日 · In Optics, Hecht, the author states that the perfect surface for a lens shape will be a hyperbola.
Relationship Between Hyperbolas and Hyperbolic Spaces
2022年2月17日 · Although I don't fully understand the math, but I think a "hyperbola" would resemble the shape of a "hourglass cone" in 3 dimensions. As the picture above shows, a triangle in Euclidean Space becomes "distorted" when projected onto a Hyperbolic Space. This is my naïve guess about the relationship between hyperbolic functions and hyperbolic spaces.
conic sections - hyperbola curve formula in 3 dimensions
If I understand correctly, any ax+by=c is a plane parallel to the z axis. In my case hyperbola has 3 known points on some unknown ax+by=c plane. If I had a formula for 3d hyperbola, I could solve a system of 3(?) equations to get coefficients for hyperbola going through my points (which is what I need to do). $\endgroup$ –
Is there a parabola which is similar to a branch of hyperbola?
2018年12月6日 · We put one vertex of the hyperbola at a fixed point and move the other vertex away, allowing the angle between the asymptotic lines to approach zero as the other vertex goes off to infinity. If we cleverly balance the rates at which the angle gets smaller and the other vertex gets farther, the hyperbolas will approach the shape of a parabola.
conic sections - Creating a Hyperbola with a Flashlight
2015年3月16日 · Ellipse is anything between circle and parabola, hyperbola is anything between parabola and parabola (remember the cone has its mirror extension above the apex and similar set of sections there). And there are degenerate sections (a point, a ray, a line and a pair of lines) obtained when the cutting plane meets the apex. $\endgroup$
Real world uses of hyperbolic trigonometric functions
2017年1月27日 · In architecture, if you have a free-standing (i.e. unloaded and unsupported) arch, the optimal shape to handle the lines of thrust produced by its own weight is $\cosh(x)$. The dome of Saint Paul's Cathedral in England has a $\cosh(x)$ cross-section. This type of arch was also favoured by architect Antoni Gaudí in his work.
What is the shape of the shadow of the rim of my lamp shade?
2020年12月8日 · Y is the radius of the cone at that particular horizontal cross-section, but since it is proportional to the height at which you are looking at, we can interchange them without having to worry about our shape changing from a hyperbola to something else. So as we proceed up, y increases linearly.
What are the interesting applications of hyperbolic geometry?
I am aware that, historically, hyperbolic geometry was useful in showing that there can be consistent geometries that satisfy the first 4 axioms of Euclid's elements but not the fifth, the infamous