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Question
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
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...

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Scott A Wilson

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I can answer any question in general math, arithetic, discret math, algebra, box problems, geometry, filling a tank with water, trigonometry, pre-calculus, linear algebra, complex mathematics, probability, statistics, and most of anything else that relates to math. I can also say that I broke 5 minutes for a mile, which is over 12 mph, but is that relevant?

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Experience in the area; I have tutored people in the above areas of mathematics for over two years in AllExperts.com. I have tutored people here and there in mathematics since before I received a BS degree back in 1984. In just two more years, I received an MS degree as well, but more on that later. I tutored at OSU in the math center for all six years I was there. Most students offering assistance were juniors, seniors, or graduate students. I was allowed to tutor as a freshman. I tutored at Mathnasium for well over a year. I worked at The Boeing Company for over 5 years. I received an MS degreee in Mathematics from Oregon State Univeristy. The classes I took were over 100 hours of upper division credits in mathematical courses such as calculus, statistics, probabilty, linear algrebra, powers, linear regression, matrices, and more. I graduated with honors in both my BS and MS degrees. Past/Present Clients: College Students at Oregon State University, various math people since college, over 7,500 people on the PC from the US and rest the world.

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My master's paper was published in the OSU journal. The subject of it was Numerical Analysis used in shock waves and rarefaction fans. It dealt with discontinuities that arose over time. They were solved using the Leap Frog method. That method was used and improvements of it were shown. The improvements were by Enquist-Osher, Godunov, and Lax-Wendroff.

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Master of Science at OSU with high honors in mathematics. Bachelor of Science at OSU with high honors in mathematical sciences. This degree involved mathematics, statistics, and computer science. I also took sophmore level physics and chemistry while I was attending college. On the side I took raquetball, but that's still not relevant.

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I earned high honors in both my BS degree and MS degree from Oregon State. I was in near the top in most of my classes. In several classes in mathematics, I was first. In a class of over 100 students, I was always one of the first ones to complete the test. I graduated with well over 50 credits in upper division mathematics.

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My clients have been students at OSU, people who live nearby, friends with math questions, and several people every day on the PC. I would guess that you are probably going to be one more.

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