We are all going to use the wiki to discuss problems assigned. Look below and you will find the problem that you are responsible to post the first answer for based on your Aquinas e-mail address. It is NOT o.k. to just write "I don't get it". Start by typing the problem (click on edit to start) word for word from the book. You Post your answer as if it were a test question ( You would not leave those blank you would take a stab at it!), HOW you got it (list specific page references and show work) and WHY you did that way. The rest of the class will make comment on at least 3 other problems, corrections, and post their thoughts below your original response. POST THE ORIGINAL RESPONSES BY 10/8 AND THE 3 RESPONSES BY 10/10
SECTION 4.5 ( 1, 2, 3, 5, 6 ,7, 11, 14, & 15)
1) [ trc002] What makes a polygon a REGULAR polygon is when it is equiangular and equilateral. 6 regular polygon
3 nonregular polygons Nice shapes - does everyone agree that the top 6 are regular polygons? Make sure you use the definition of regular polygon to make your decision. [Slewis]
Chris. I agree that they look like regular polygons to me.
What is the exact definition to a regular polygon?
2) [ jtl001]
-What makes a solid a regular (platonic) solid?
-A solid is a platonic solid if it is made up of flat sides as symmetrical as possible, its faces should be identical regular polygons, and the number of edges coming out of any vertex of the solid should be the same for all vertices.
-page 270-271
How symmetrical is "as symmetrical as possible"? Anyone can answer this. [SLewis]
Klk002,COMMENT: ... having corresponding points whose connecting lines are bisected by a given point or perpendicularly bisected by a given line or plan.
3) [ klk002]
- How many faces, edges and vertices are there in a cube and a tetrahedron ?
Cube:
-6 Faces
-12 Edges
-8 Vertices How can that be? A cube has square faces so they each have 4 edges and six faces total, that should be 24 edges. [SLewis] OOPS --- 6 faces, 24 edges and 8 vertices for a cube. klk002
Tetrahedron:
-4 Faces
-12 Edges
-4 Vertices
5) [ ljj001]
jtloo1 Comment: the first is a tetrahedron, second is a irregular polyhedron, and third is a octahedron.
6) [ CSV001]
I do not have the resources to make a "Platonic Solid Kit"
This is hardly a question. I agree I was left confused. There is no question you just have to build a set of solid and I do not have the materials to make this. Were we really suppose to do a different one besides #6?~uraqtinvu
7) [JEH003]
11) [nmg002] *They all have an answer of 2* TETRAHEDRON 4-6-+4=2 CUBE:8-12+6=2 OCTAHEDRON:6-12+8=2 DODECAHEDRON:20-30+12=2 ICOSAHEDRON:12-30+20=2
14) [fab001]
The solids are: If we cut them we get:
Tetrahedron Triangle
Cube Square
Octahedron Square
Dodecahedron Triangle
Icosahedron Pentagon
jtl001 comment: for a cube, don't you get a triangle if you slice a vertex?
15) [mrh003]
Sliding on the cube: Suppose we start the the edges of a cube (that is, its skeleton). Now, on each square face, we glue four triangles together as shown at the right. Count the number of its vertices, edges, and faces.
Vertices: 12
Edges: 36
Faces: There are six faces to the cube and four triangles on each face so there are 24 faces.
POST THE ORIGINAL RESPONSES BY 10/8 AND THE 3 RESPONSES BY 10/10
SECTION 4.5 ( 1, 2, 3, 5, 6 ,7, 11, 14, & 15)
1) [ trc002] What makes a polygon a REGULAR polygon is when it is equiangular and equilateral.
3 nonregular polygons
Nice shapes - does everyone agree that the top 6 are regular polygons? Make sure you use the definition of regular polygon to make your decision. [Slewis]
Chris. I agree that they look like regular polygons to me.
What is the exact definition to a regular polygon?
2) [ jtl001]
-What makes a solid a regular (platonic) solid?
-A solid is a platonic solid if it is made up of flat sides as symmetrical as possible, its faces should be identical regular polygons, and the number of edges coming out of any vertex of the solid should be the same for all vertices.
-page 270-271
How symmetrical is "as symmetrical as possible"? Anyone can answer this. [SLewis]
Klk002,COMMENT: ... having corresponding points whose connecting lines are bisected by a given point or perpendicularly bisected by a given line or plan.
3) [ klk002]
- How many faces, edges and vertices are there in a cube and a tetrahedron ?
Cube:
-6 Faces
-12 Edges
-8 Vertices
How can that be? A cube has square faces so they each have 4 edges and six faces total, that should be 24 edges. [SLewis]
OOPS --- 6 faces, 24 edges and 8 vertices for a cube. klk002
Tetrahedron:
-4 Faces
-12 Edges
-4 Vertices
5) [ ljj001]
jtloo1 Comment: the first is a tetrahedron, second is a irregular polyhedron, and third is a octahedron.
6) [ CSV001]
I do not have the resources to make a "Platonic Solid Kit"
This is hardly a question.
I agree I was left confused. There is no question you just have to build a set of solid and I do not have the materials to make this. Were we really suppose to do a different one besides #6?~uraqtinvu
7) [JEH003]
11) [nmg002] *They all have an answer of 2*
TETRAHEDRON 4-6-+4=2
CUBE:8-12+6=2
OCTAHEDRON:6-12+8=2
DODECAHEDRON:20-30+12=2
ICOSAHEDRON:12-30+20=2
14) [fab001]
The solids are: If we cut them we get:
Tetrahedron Triangle
Cube Square
Octahedron Square
Dodecahedron Triangle
Icosahedron Pentagon
jtl001 comment: for a cube, don't you get a triangle if you slice a vertex?
15) [mrh003]
Sliding on the cube: Suppose we start the the edges of a cube (that is, its skeleton). Now, on each square face, we glue four triangles together as shown at the right. Count the number of its vertices, edges, and faces.
Vertices: 12
Edges: 36
Faces: There are six faces to the cube and four triangles on each face so there are 24 faces.