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
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