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The shape can be constructed by taking a cylinder with its height equal to its diameter and cutting a triangle out of it when viewing it from the side with the base of the triangle matching one end of the cylinder and the opposite point of the triangle in the center of where the opposite end of the cylinder was.

Is there a name for this shape?

m_duran
  • 121

5 Answers5

12

Like this?

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It has three Forms depending from which side you look:

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3

It is called a chisel tip. A round chisel. However, not all chisels are round.

Sohail Si
  • 375
2

The shape displayed in Julien Kluge's answer may be seen as a special version of a cylindrical segment, which MathWorld describes as the solid cut from a circular cylinder by two (or more) planes. In any case, it can be made by removing two cylindrical hooves from a cylinder. No idea whether there is a distinctive name for what is left, but the name cylindrical wedge is already reserved for the version with only one slanted cut through the cylinder base, examples of which are the cylindrical hooves mentioned above.

ccorn
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2

MathWorld gives the name "Cork plug" for "a three-dimensional solid that can stopper a square, triangular, or circular hole. There is an infinite family of such shapes. The shape with smallest volume has triangular cross sections."

Further,

The plug with the largest volume is made using two cuts from the top diameter to the edge [...]. Such a plug [with height $h$ and radius $r$] has $h=2r$ to obtain a square cross section. For a general such a plug of height $h$ and radius $r$, the volume of the plug is

$$V = \frac13(3\pi-4)hr^2$$

The entry cites Martin Gardner's book "The Second Scientific American Book of Mathematical Puzzles and Diversions" (UC Press, 1987). The term comes from the section "The Cork Plug", in which Gardner writes

Many old puzzle books explain how a cork can be carved to fit snugly into square, triangular and square holes. An interesting problem is to find the volume of the cork plug. [...]

See, for instance, this 2009 discussion (via harvard.edu) supplementing Oliver Knill's Multivariable Calculus course at Harvard.

Blue
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0

For a circular base it is like a pencil lead sharp chisel line edge cut/ground by sandpaper that way for drawing thin lines. Elliptic arc intersection lines on side view appear together with square border.

Narasimham
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