Someone recently gave me an advice, he said, "When your young child asks you something, find an answer for him immediately. Don't tell him to come back later, cos he won't ask you again." I'm guilty of often shoo-ing Sean away when he comes to me with questions.
This evening, he asked, "Why isn't a sphere a platonic solid?". I remember shoo-ing him away weeks back when he asked me this exact question, so it's not true that they won't ask again hehe. Still, the above is good advice to take on board, and so I dutifully googled the answer.
Firstly, I asked Sean what a platonic solid was cos really, I have no idea. His reply, "A polyhedron where all the faces are regular polygons and all the corners have the same number of faces joining them and all the faces are exactly the same size and shape and they certainly don't wear trainers." Whhhhat???
So I find pictures of Platonic Solids on the internet and there are just 5 of them. I shout out to Brian asking him if he knew what Platonic Solids were. He comes over and says, "Well, the Greeks believed that these were the shapes that made the four elements and the universe."
Are you surrre?...I ask.
Yeah, and he points to the 5th Platonic Solid (PS) up there and says, "This is the Universe."
Sean immediately jumps in, "No it's not. The Dodecahedron is the Universe.", pointing to the 4th PS. Brian says, "Oh...yeah."
And kiasu Sean fearing his brother would name the rest, blurts out quickly, "The tetrahedron is Fire, the cube is Earth, the Octohedron is Air and the Icosahedron is the Water. The Dodecahedron represents the entire Universe."
Brian returns to where he came from and I go back to Sean's original question. I asked him why he thought a sphere should be a platonic solid, he says, "It's a kind of solid, a regular solid. That's all."
Some googling later, we find out, a sphere isn't even a polyhedron! So by the definition Sean gave up there, of course the sphere can't be a platonic solid, since it isn't even a polyhedron in the first place.
When I told Sean a sphere isn't a polyhedron, he asks, "Why not?" er...one can argue it is a polyhedron with infinite numbers of faces and vertices...but let's not go there.
So mathematicians say a sphere is not a polyhedron and it has no face (it does have a surface).
From Wikianswers: "A polyhedron is a 3 dimensional figure made up of polygons. We use the term 'face' to refer to these polygons. Since a sphere is not a polyhedron, we mathematicians consider it to have no faces."
Similarly, a circle isn't a polygon and has no sides. Really? Did they teach us this in school?? Was I sleeping in class??
I shout out to Brian again and asked, "Did you know that a circle isn't a polygon."
He says, "Of course. A polygon has to have straight sides so a circle isn't a polygon."
Okayyyy "So a circle is just a shape?"
"Yes, shapes include polygons but shapes aren't necessarily polygons. And polygons can't have holes in them, so a square with a hole in the middle isn't a polygon."
"So a semicircle isn't a polygon?"
"No Mummy...and neither is a ring." (rather impatiently)
"Yes, a ring, a circle within a circle, a flat Torus."
"Torus...a doughnut shape, like a ring."
Now it's my turn to be sassy, "Of course it's not lah. It doesn't even have straight sides."