Dear friends:
The graph of the equation
f(x, y) = 0
gives rise to many interesting curves in the plane for different choices of the function.
One such choice of f(x, y) led me to the following graph of the equation f(x, y) = 0.
I have the following questions:
1) Can you name this geometric shape?!
What does it remind you of?
2) Any noticeable symmetry property?!
Thank you for your thoughts.
Best wishes
Sundar
Thanks for your reply!
This closed curve exhibits point reflexion symmetry about the origin.
I wish to find a name for it but no luck so far.
Is there any real-life object that resembles the figure above?!
A geometric shape is the geometric information which remains when location, scale, orientation and reflection are removed from the description of a geometric object.[1] That is, the result of moving a shape around, enlarging it, rotating it, or reflecting it in a mirror is the same shape as the original, and not a distinct shape.
Objects that have the same shape as each other are said to be similar. If they also have the same scale as each other, they are said to be congruent.
Many two-dimensional geometric shapes can be defined by a set of points or vertices and lines connecting the points in a closed chain, as well as the resulting interior points. Such shapes are called polygons and include triangles, squares, and pentagons. Other shapes may be bounded by curves such as the circle or the ellipse.
Many three-dimensional geometric shapes can be defined by a set of vertices, lines connecting the vertices, and two-dimensional faces enclosed by those lines, as well as the resulting interior points. Such shapes are called polyhedrons and include cubes as well as pyramids such as tetrahedrons. Other three-dimensional shapes may be bounded by curved surfaces, such as the ellipsoid and the sphere.
A shape is said to be convex if all of the points on a line segment between any two of its points are also part of the shape.
@ Adriana,
Could you please stop copy paste answers.
See the attached file.
Dear Sundarapandian,
It seems to be a limit cycle.
Could you please read the attached conference paper.
It includes the same shape that appeared as a limit cycle for the companion dynamical system.
Hope it helps.
Best wishes
Dear Sundarapandian Vaidyanathan,
- Note added: In French, it is called rectangle curviligne .
Your point [0,0] is a center of symmetry.
you can call it "AXE " function , it looks to some extent like the blade of an axe.
I thank all for your answers.
Especially, I like to thank Debopam Ghosh - it does look like the blade of an axe. Thanks a lot!
Respected Sundarapandian,
In my knowledge, I could not understand what is the shape of this curve exactly. Could send the corresponding conference paper, I will study if you are willing.
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