Questions tagged [parametric]
For questions about parametric equations, their application, equivalence to other equation types and definition.
2,627 questions
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Parametric equation of straight line
I know that the parametric equation of a straight line is given in the form of $$\frac{x-x_1}{\cos\theta} = \frac{y-y_1}{ \sin\theta}=r,$$
where $(x_1,y_1)$ is some fixed point and $r$ the distance of ...
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find a parametrization for a cube
In $\mathbb R^2$, the contour $C:$
\begin{align}
\max\big(|x|,|y|\big) &= c
\\ \Leftrightarrow |x-y|+|x+y|&=2c
\end{align}
of a square can be given with a parametrization
$$c\cdot\left( \...
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What is an equation for rounded square with smooth corner and no flat sides? What is this attempt of mine?
What are
intuition or geometric explanations
simple examples
plots or references
for an equation (any form — implicit, parametric, or polar) for a curve that
has overall shape similar to a square
...
- 153
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What is the cartesian equation for the graph of the parametric curve $(x,y)= ( t^{\frac{1}{1-t}},\, t^{\frac{t}{1-t}}) $?
The parametric curve
$$ \left( t^{\frac{1}{1-t}},\, t^{\frac{t}{1-t}}\right) $$
for $t \in (0,1)\cup(1,\infty)$ traces out the points on the graphs of $y = x^t$ which are furthest from the line $y = x$...
- 7,646
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Parametric leaf profile?
I am trying to look for a nice way of parametrizing a leaf (botanical) profile. First a regular leaf, but I also would like to do an oak. The trivial answer is to use a B-Spline, but for multiple ...
- 3,957
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Is there a trick to finding the normal function of an ellipse given its parametric definition?
I’m trying to solve a calculus problem posed like this (N is the unit normal function and T is the unit tangent function):
Use the formula $\textbf{N} = \frac{d\textbf{T}/dt}{|d\textbf{T}/dt|}$ to ...
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Is it possible to calculate the volume of a general 3D (closed & convex) parametric surface?
I have three parametric equations in two variables that give the coordinates of points on a three-dimensional, closed, convex surface. I want to find the volume enclosed by that surface, but I haven't ...
- 2,516
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Waggle-Dance Equation 🐝
Once a foraging bee finds food, it returns to the hive and communicates the location of the food source to the colony using the elegant waggle dance.
Bees interpret this dance by combining their ...
- 1,228
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How do i modify these skewed vectors to intersect?
Essentially, my question is to modify my current equations (that are skewed for now) to set up a situation where one drone intercepts the other, to find k. where one drone is assigned as an “attack ...
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Finding the parametric equation of a line in three dimensions
Problem:
Find the parametric equation for the line through $P(-2,0,3)$ and $Q(3,5,-2)$.
Answer:
\begin{align*}
\overrightarrow{PQ} &= ( 3 - -2 )i + (5 - 0 ) j + (-2 -3 )k \\
\overrightarrow{PQ} &...
- 4,644
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4
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Determine $m \in \mathbb Z$ for which $x_1, x_2\in \mathbb Z$ [closed]
Consider the equation $(m-1)x^2-(3-m)x-m=0$ with m real numbers $m$ different from $1$, having roots $x_1, x_2$.
Determine $m \in \mathbb Z$ for which $x_1, x_2\in \mathbb Z$.
my ideas
So I was able ...
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Does a parametric linear feasibility program with polynomial constant term have a polynomial solution?
Let $A \in \mathbb{R}^{m \times q}$. Let $b:\mathbb R^n \rightarrow \mathbb R^{m}$ be a polynomial function homogeneous of degree 2 (i.e., $b(z) = H (z\otimes z)$, for some matrix $H$), of a variable ...
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How do I convert this parametric curve into an implicit curve? [closed]
I have a continuous closed parametric curve
$$
\begin{align}
x &= \arccos\left(-\frac{Q × \sqrt{\frac{1}{3}} \left(\tan\left(\frac{π}{4} u\right)^2 - 1\right) - \sqrt{\frac{2}{3}} \left(\tan\left(\...
- 2,516
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Find all values of $k\in\Bbb R$ for which $(k-1)x^3 - 4x^2 + (k+2)x$ has two roots
That's problem statement:
Find all values of $k\in\Bbb R$ for which the polynomial $W(x) = (k-1)x^3 - 4x^2 + (k+2)x$ has an even number of roots.
We factorize by $x$, so we get $W(x) = x[(k-1)x^2 - ...
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Every odd function has a corresponding involution
Consider functions $f$ which are involutions, i.e.
\begin{align}
f(f(x))=x\quad \implies \quad f'(x)f'(f(x))=1.
\end{align}
Under the (Legendre-like) contact transformation
\begin{align}
f(x)=F'(X),\ ...
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