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Name of Truncated Circle

Date: 12/29/2003 at 13:29:45
From: Paul 
Subject: Name of "oval" with straight sides???

What is the name of a rectangle with two rounded ends, like a circle 
with top and bottom evenly truncated?  For example, an "oval"
racetrack with two straightaways on opposite sides, parallel to each
other and both of the same length.  I know that's not really an oval,
but I'm not sure what else to call it!

The truncated circle still has "corners", the "racetrack" shape would 
not--unless one really wants the drivers to have a hard time!  I am 
more interested in the truncated circle, but the "racetrack" shape is 
of interest, also.  I just need the name.  Thank you!



Date: 12/29/2003 at 14:00:23
From: Doctor Douglas
Subject: Re: Name of "oval" with straight sides???

Hi Paul,

For a shape with corners, the term "truncated circle" is fine.  I've 
not come across any other specific term for this shape.  However, the 
3-dimensional analogue of this shape is called a "spherical segment":

   Ask Dr. Math FAQ:  Sphere Formulas
    http://mathforum.org/dr.math/faq/formulas/faq.sphere.html#spheresegment

and hence your 2-dimensional geometric shape could also be described
as the "cross-section of a spherical segment".

For a shape without corners I have seen the term "racetrack" used
informally.  In some branches of mathematical physics, the term
"stadium" or "stadium shape" is used.  The curved pieces are
semicircles whose diameter is equal to the width of the rectangle.
The length of the rectangle is not specified. 

I hope this answers your question!

- Doctor Douglas, The Math Forum
  http://mathforum.org/dr.math/ 



Date: 12/29/2003 at 14:44:04
From: Paul 
Subject: Name of "oval" with straight sides???

Dear Dr. Douglas,

Thanks for your FAST answer--that helps!  Since we are talking 3-
dimensional now, what would you call a vertical cylinder that has (for 
example) 20% of opposite (vertical) sides truncated?  (You would see 
the truncated circle looking down at it.)  Just a "vertical cylinder 
with opposing truncated sides"?  This is a common actual mechanical 
part -- even more common is a cylindrical shaft with ONE side 
truncated. What's that called?
 
                              Thanks again!

                              Paul



Date: 12/29/2003 at 16:00:52
From: Doctor Douglas
Subject: Re: Name of "oval" with straight sides???

Hi again, Paul.

Usually the term that is used to go into the third dimension is
"prism", but this term is usually reserved for polygonal bases (e.g.
rectangular prism, hexagonal prism).  

A circular prism is called a cylinder, and by analogy with the segment
of a circle, we may call the once-sliced shaft a "cylindrical segment":

  Cylindrical Segment
    http://mathworld.wolfram.com/CylindricalSegment.html 

I don't know the proper term for the cylinder with two opposing slices
taken from it.  I actually use this shape in some of my engineering
work where a part is internally threaded but needs two flats for a
wrench to grip it.  It therefore functions as a nut.  If I were to
invent a name for this shape, I might use "para-truncated cylinder",
where "para-" indicates that the two truncated surfaces are opposite
each other.  This is consistent with the way certain chemicals are
named.  

- Doctor Douglas, The Math Forum
  http://mathforum.org/dr.math/ 


Date: 12/29/2003 at 16:19:37
From: Paul 
Subject: Name of "oval" with straight sides???

Dear Dr. Douglas,

     You are pretty close on the application!  "Para-truncated
cylinder" sounds good to me and will probably impress everybody.
Thanks much!  I'll refer your site to some of my friends.

                             Best Regards,

                             Paul
Associated Topics:
College Geometry
College Higher-Dimensional Geometry
High School Geometry
High School Higher-Dimensional Geometry
High School Practical Geometry

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