Subject: Octagonal protect against Sign Name: Phil Who room you: Teacher
Hello! my colleagues and also I room in a discussion around how numerous true "sides" one octagonal stop sign has. Ns say the it has actually 10 true sides due to the fact that of the front earlier sides the a protect against sign (3D octagon). Is this correct terminology or have to the former and back "sides" be described as encounters -- equaling 2?
By math definition, one octagon is one 8 sided 2-D shape. A prevent sign, technically, is no 2-D, so that is no an octagon. A avoid sign is 3-D, and also has 10 faces. We could consider only the front challenge of a protect against sign, which would be one octagon (now, we room ignoring the thickness of the sign, and it has actually 8 sides). It is typical place to describe a avoid sign as an octagon, since it has actually 8 edges approximately it"s front face - this is unshened language that is fine because that day-to-day communication, yet is no acceptable in in ~ the specific language that mathematics.
I agree totally with Paul"s an answer but I desire to include something. An octagon is one 8 sided 2-D shape yet in explicate the 3-D "stop sign" form (I drew one below that is thick enough that you have the right to see the third dimension) mathematicians usage the terms vertices, edges and also faces.
I have always thought the they carry out so precisely since the term "side" tote connotations in English that provide rise to exactly the ambiguities that you and your partner detected.
my 2 cent worth:
Technically, a "side" is not a mathematically specific term, for this reason mathematicians avoid it. However, also we usage the term "side" in the same loosened way that everyone else does, therefore really we are in search of a bridging meaning that offers more precision for words "side" there is no breaking any kind of of the conventional linguistic meanings.
I would propose the a "side" be one measurement less 보다 the object whose side it is. Because that example, the side of an octagon is 1 measurement (so the is part of a line) since an octagon is a 2 dimensional shape. A side of a cube is a two-dimensional shape (part that a plane).
Curved surface still attitude a problem and also although us could continue to filter our definition, I intend shapes like the möbius strip and the Klein party will continue to vex us. Look this up if you room curious about why.