algebra precalculus - Why do all parabolas have an axis of …
May 30, 2015 · In that case we can show generally that every conic section must have an axis of symmetry: Consider the axis of the cone. If it is perpendicular to the plane, the conic section is …
How do we prove that a parabola has only one axis of symmetry?
Dec 21, 2024 · A line can only be an axis of symmetry of a conic if it is perpendicular to the conic at each point of intersection between the line and the conic. If this has not already been …
Finding the order of rotational symmetry about a given axis
Mar 13, 2022 · Here is the only example my book gives about rotational symmetry about an axis: I am then asked to find the order of rotational symmetry for the following solids: I think (a) (b) …
Pentagon axis of symmetry - Mathematics Stack Exchange
The axis of symmetry in a regular pentagon is the segment drawn from a vertex to the midpoint of the opposite side. If this is true, I don't see how it would pass through more than one vertex at …
geometry - How many axis of symmetry of the cube are there ...
May 10, 2017 · Nine symmetries looks right to me, once you restrict to 180 degree rotations. For any axis of symmetry according to your definition is also an axis of a rotation in the more …
Parallelograms & Axis of Symmetry - Mathematics Stack Exchange
An axis of only- (b) symmetry contains all the vertices, making them collinear (but in a different arrangement than required by (a)). If you disallow "degenerate" parallelograms with all vertices …
What does it mean for a function to be oddly and evenly symmetric?
Sep 12, 2021 · If a function has symmetry about the x axis we reflect off the y axis check if there is a match in corresponding values then we get an even match on both sides then the function …
Identify the symmetries and sketch the curve $r=\sin (\theta/2)$
May 5, 2018 · The equation has failed the symmetry test, but that does not mean that the graph is not symmetric with respect to x-axis. As a matter of fact if passing a symmetry test verifies that …
What is the relation between the principal axes (of inertia) and the ...
2 If a homogeneous 2D shape has an axis of symmetry, then this axis is also a principal axis of inertia: this is a general result, which can be proved as follows. Let's take an orthogonal …
Rotational Symmetries of a Cube - Mathematics Stack Exchange
Hence the stabilizer of a vertex under rotations of the cube consists of three elements: 1. the identity rotation (by 0 0 or 2π 2 π or −24π 24 π, it's all the same symmetry), 2. rotation about …