logistic_guy
Full Member
- Joined
- Apr 17, 2024
- Messages
- 319
here is the question
Parametrize the surface (catenoid) that is formed when rotating the curve \(\displaystyle x = \cosh z\) around the \(\displaystyle z\)-axis.
my attemb
i think they want me to find the map \(\displaystyle \boldsymbol{\rho}: C \to \mathbb{R}^3\), where \(\displaystyle C \subset \mathbb{R}^2\)
i'm very good in differential geometry but it's shocking i can't visualize this curve. the variables \(\displaystyle x\) and \(\displaystyle z\) is confusing written together. i learn years ago in calculus solid of revolution and the function \(\displaystyle y = \cosh x\) is easy to visualize. when i rotate this function around \(\displaystyle y\)-axis i get volume, its surface called catenoid. so i think this related to the original question but i can't go
from \(\displaystyle y = \cosh x\) to \(\displaystyle x = \cosh z\) to the parametrize
Parametrize the surface (catenoid) that is formed when rotating the curve \(\displaystyle x = \cosh z\) around the \(\displaystyle z\)-axis.
my attemb
i think they want me to find the map \(\displaystyle \boldsymbol{\rho}: C \to \mathbb{R}^3\), where \(\displaystyle C \subset \mathbb{R}^2\)
i'm very good in differential geometry but it's shocking i can't visualize this curve. the variables \(\displaystyle x\) and \(\displaystyle z\) is confusing written together. i learn years ago in calculus solid of revolution and the function \(\displaystyle y = \cosh x\) is easy to visualize. when i rotate this function around \(\displaystyle y\)-axis i get volume, its surface called catenoid. so i think this related to the original question but i can't go
from \(\displaystyle y = \cosh x\) to \(\displaystyle x = \cosh z\) to the parametrize