I do not understand why when you revolve a hyperbola around a circle the respective parameters (cosh (v) and cos (u)) are multiplied by each other to get the parametric form of the hyperboloid. I would greatly appreciate it if someone could show me how these parameters are reached.
2025-01-13 03:02:22.1736737342
Parametrizaction of a Hyperboloid
160 Views Asked by user314618 https://math.techqa.club/user/user314618/detail At
1
There are 1 best solutions below
Related Questions in PARAMETRIC
- Parametric line segment in 3-space
- Finding an equation relating $x$ and $y$ with their respective parametric equations and using its differential?
- Area of parametric surface (theory)
- Trigonometric equation with parameter
- Parametrics, when $t$ is not in between $0<t<1$
- Parameterization of an ellipse
- Is there a general equation for an n-ellipse?
- On my grapher, $(\cos t, \sin (t+1))$ generates a geometric figure. What is that figure?
- Parametric curve: $x=\frac{a}{2}(t+\frac{1}{t})$, $y=\frac{b}{2}(t-\frac{1}{t})$?
- Is this parametric equation describe a circle?
Related Questions in HYPERBOLIC-GEOMETRY
- Triangle inequality of hyperbolic metric
- Is the tangent bundle of hyperbolic space trivial?
- Outer Automorphisms of PSL2(R)
- Finitely Many genus-g Quotients of Compact Riemann Surface
- Applications of the Hurwitz Theorem on Number of Automorphisms?
- Why does the halfplane model of the hyperbolic plane involve only the upper half of the plane?
- "Every geometry is a projective geometry." So is hyperbolic geometry a projective geometry?
- Algebraic solutions for Poincaré Disk arcs
- The precise formula of the Poincare-Bergman metric on the disc $\mathbb{D}$.
- Law of Cosines with imaginary arguments?
Related Questions in PARAMETRIZATION
- I don't understand why we represent functions $f:I \subseteq \Bbb R \to \Bbb R^2$ the way we do.
- Parametrization of intersection of curves
- Parametric line segment in 3-space
- Parametrizing a surface with a single parameter.
- How to reparametrize with respect to arc length?
- Is there a way to parametrise general quadrics?
- Parametrization of $a^2+b^2+c^2=2d^2$
- How to prove that a curve is an injective regular parameterization?
- Parametrization of a rotating surface
- How to parametrize the surface $x^3 + 3xy + z^2 = 2$ and compute a tangent plane
Related Questions in QUADRICS
- Is there a way to parametrise general quadrics?
- A circular paraboloid can be a elliptic paraboloid?
- Classify the surface $x^2 + y^2 - z^2 + 2xy - 2xz - 2yz - y = 0$
- Change the variables in $Q(x,y,z)=(x-y+z-1)^2-2z+4$ to have $Q(f(u,v,w))=u^2+v$
- One-Sheet Hyperboloid: Find the equation given the figure
- Points with constant polar w.r.t to a tangent conic bundle
- Parametrizaction of a Hyperboloid
- How to find the equation of the curve defining the intersection of two quadrics.
- Linear Map of an ellipsoid in $\mathbb{R}^N$ into another ellipsoid in $\mathbb{R}^n$, with $n<N$
- Find an orthogonal Matrix to a quadric
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Refuting the Anti-Cantor Cranks
- Find $E[XY|Y+Z=1 ]$
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- What are the Implications of having VΩ as a model for a theory?
- How do we know that the number $1$ is not equal to the number $-1$?
- Defining a Galois Field based on primitive element versus polynomial?
- Is computer science a branch of mathematics?
- Can't find the relationship between two columns of numbers. Please Help
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- A community project: prove (or disprove) that $\sum_{n\geq 1}\frac{\sin(2^n)}{n}$ is convergent
- Alternative way of expressing a quantied statement with "Some"
Popular # Hahtags
real-analysis
calculus
linear-algebra
probability
abstract-algebra
integration
sequences-and-series
combinatorics
general-topology
matrices
functional-analysis
complex-analysis
geometry
group-theory
algebra-precalculus
probability-theory
ordinary-differential-equations
limits
analysis
number-theory
measure-theory
elementary-number-theory
statistics
multivariable-calculus
functions
derivatives
discrete-mathematics
differential-geometry
inequality
trigonometry
Popular Questions
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- How to find mean and median from histogram
- Difference between "≈", "≃", and "≅"
- Easy way of memorizing values of sine, cosine, and tangent
- How to calculate the intersection of two planes?
- What does "∈" mean?
- If you roll a fair six sided die twice, what's the probability that you get the same number both times?
- Probability of getting exactly 2 heads in 3 coins tossed with order not important?
- Fourier transform for dummies
- Limit of $(1+ x/n)^n$ when $n$ tends to infinity
I'm guessing a bit at the description you're looking at, but I think you're looking at $$ (\cosh (v) \cdot \cos (u), \cosh (v) \cdot \sin (u), \sinh(v)) $$
Think of your hyperbola in the $x,z$ plane, and think about what happens when you rotate a single point on the hyperbola around the $z$-axis, say $$(\cosh(v),0,\sinh(v))$$ Well, it's a circle of radius $\cosh(v)$ maintaining a height of $\sinh(v)$. So the $z$ coordinate stays fixed, and the $x,y$ coordinates pass through $(\cos(u)\cdot\cosh(v),\sin(u)\cdot\sinh(v))$. I'm not great at describing these things without chalk, but does that make sense?