Subject: Octagonal protect against Sign Name: Phil Who are you: Teacher
Hello! mine colleagues and also I room in a discussion around how plenty of true "sides" an octagonal avoid sign has. I say that it has 10 true sides due to the fact that of the front ago sides the a protect against sign (3D octagon). Is this exactly terminology or have to the front and back "sides" be described as deals with -- equaling 2?
By mathematics definition, an octagon is an 8 sided 2-D shape. A stop sign, technically, is no 2-D, so the is not an octagon. A protect against sign is 3-D, and also has 10 faces. Us could think about only the front challenge of a avoid sign, which would be one octagon (now, we are ignoring the thickness that the sign, and it has actually 8 sides). That is usual place to describe a prevent sign together an octagon, due to the fact that it has 8 edges approximately it"s front confront - this is not blocked language that is fine for day-to-day communication, however is no acceptable in within the specific language the mathematics.
I agree totally with Paul"s solution but I want to include something. An octagon is an 8 face 2-D shape but in describing the 3-D "stop sign" shape (I drew one listed below that is thick sufficient that you can see the 3rd dimension) mathematicians use the terms vertices, edges and faces.
I have constantly thought that they perform so precisely since the term "side" tote connotations in English that offer rise to specifically the ambiguities the you and your colleagues detected.
my 2 cent worth:
Technically, a "side" is no a mathematically precise term, therefore mathematicians protect against it. However, even we use the term "side" in the same loose way the everyone rather does, for this reason really we are searching for a bridging definition that offers much more precision for words "side" without breaking any type of of that is conventional linguistic meanings.
I would certainly propose that a "side" be one dimension less than the object whose side it is. For example, the side of one octagon is 1 dimension (so that is component of a line) because an octagon is a 2 dimensional shape. A next of a cube is a two-dimensional form (part the a plane).
Curved surfaces still pose a problem and although us could proceed to filter our definition, I mean shapes like the möbius strip and also the Klein party will continue to vex us. Look this up if you space curious about why.