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Dear Prof Scott

en.wikipedia.org/wiki/Concentric

Other then Concentric circles, spheres. semi circles , which other circular shapes can be constructed concentric ?.

As a example - Concentric cone, Inverted Concentric cone, concentric parabola, concentric ellipse, concentric hyperbola etc ?.

Also can we also have concentric shapes for Lines shapes viz Kite, Trapezoid, Rhombus, Parallelogram etc

Thanks & Regards,
Prashant S Akerkar

Answer

Expanding and Shifting
The only other circular shape I can think of is the outline of a piece of pie,
and it can be used to construct concentric shapes as well.

Since you have concentric cones and inverted concentric cones, there are also
inverted concentric parabolas.  Note that ellipses as hyperbolas include their own concentric shapes if done around their center.  If they are done around another point, they give the same function in a different location.

Yes, we can also construct concentric shapes for kites, trapezoids, rhombuses, and parallelograms.

There are also pentagons (5 sided), hexagon (6 sided), septagons (7 sided?), octagons (8 sided, and whatever other term like maybe a decagon (10 sided?), dodecagon (20 sided?), or whatever other term we can used.

Note that they can be constructed in several ways.  If the center is at the origin, they can be multiplied by some factor a little bigger than one to get an increasing size figure and number a little less than one to a decreasing size figure.  If a constant is added in the x direction, they will shift to the left or to the right.  If a constant is added in the y direction, they will shift up and down.  Both of these shifts will be uniform.  If a function is added, the way they shift could go in any sort of way.

This could affect it differently in differing directions.  Ways of doing it result in a parabolic, stepwise (where only one side changes at a time), sinusoidal (where it goes in and out), or exponential (increases {or decreases} at a faster {or slower} rate each time.

Note that if they are moved in a sinusoidal way, if the constant they vary by is a multiple of pi, the number of curves will repeat after awhile.  If the number is not a multiple of pi, eventually the curve will cover everything from k to -k where k is the multiplier.

They could also be done to be rotational.  For example, consider a square being increased in size and rotated.  The rotations could be done using cylindrical or spherical format.

Yes, there is truly a lot a know about this, but I never really thought about it before.

I also tried to include a rotational, but can't quite get it to do it right.
Maybe if this is sent back, I'll have it by then...
Questioner's Rating
 Rating(1-10) Knowledgeability = 10 Clarity of Response = 10 Politeness = 10 Comment Dear Prof Scott Thanks. Thanks & Regards, Prashant S Akerkar

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