Question 1

Group the objects into classes so that all the elements within each class are topologically equivalent and no elements from different classes are topologically equivalent.
A. a glass
B. a bowling ball
C. a sheet of typing paper
D. a ruler
E. a sphere

Accepted Answer

A glass, a bowling ball, a sheet of typing paper, and a sphere are all topologically equivalent to a sphere. A ruler is topologically equivalent to a cylinder.

Question 2

Let X be a point obviously outside the figure. Draw  . How many times does it cross the curve? ​  ​

Accepted Answer

Since the point X is outside the figure, and the curve encloses the figure, any line that passes from X to infinity will intersect the curve an odd number of times. This is a result of the Jordan Curve Theorem.

Question 3

Group the objects into classes so that all the elements within each class are topologically equivalent and no elements from different classes are topologically equivalent.

Accepted Answer

A; B AND D; C

Question 4

Group the figures into classes so that all the elements within each class are topologically equivalent, and no elements from different classes are topologically equivalent.

Accepted Answer

The answer of Group the figures into classes so that...

Question 5

Let X be a point obviously outside the figure. Draw  . How many times does it cross the curve?
​  ​
It will cross the curve an __________ (even, odd) number of times.

Accepted Answer

The answer of Let X be a point obviously outside...

Question 6

Group the figures into classes so that all the elements within each class are topologically equivalent, and no elements from different classes are topologically equivalent.

Accepted Answer

The answer of Group the figures into classes so that...

Question 7

Group the objects into classes so that all the elements within each class are topologically equivalent and no elements from different classes are topologically equivalent.
A. a bolt
B. a brick
C. a horseshoe
D. a pencil

Accepted Answer

The answer of Group the objects into classes so that...

Question 8

Determine whether each of the points A, B, and C is inside or outside of the simple closed curve.
​  1. Point C
2. Point A
3. Point B
a. outside
b. inside
​
-C

Accepted Answer

The answer of Determine whether each of the points A,...

Question 9

Group the objects into classes so that all the elements within each class are topologically equivalent and no elements from different classes are topologically equivalent.
A) a bolt
B) a straw
C) a sewing needle
D) a funnel with a handle

Accepted Answer

The answer of Group the objects into classes so that...

Question 10

Group the objects into classes so that all the elements within each class are topologically equivalent and no elements from different classes are topologically equivalent.
A) a glass
B) a bowling ball
C) a sheet of typing paper
D) a sheet of two-ring-binder paper
E) a sphere

Accepted Answer

The answer of Group the objects into classes so that...

Question 11

Let X be a point obviously outside the figure. Draw  . How many times does it cross the curve? ​  ​

Accepted Answer

Since the point X is outside the figure and the curve enclosing the figure is a closed loop, any line drawn from X to infinity must cross the curve an odd number of times, by the Jordan Curve Theorem. Therefore, the answer is A, it will cross the curve an odd number of times.

Question 12

Let ​X be a point obviously outside the figure. Draw  . How many times does it cross the curve?
​  ​
It will cross the curve an __________ (even, odd) number of times.

Accepted Answer

The answer of Let ​X be a point obviously outside...

Question 13

Read the poem in the News Clip.  Is a right-handed mitten topologically equivalent to a left-handed mitten? Answer yes or no.
If a right-handed mitten is turned inside out, as is suggested in the poem, will it still fit a right hand? Answer yes or no.

Accepted Answer

The answer of Read the poem in the News Clip....

Question 14

Determine whether the graph is a tree.

Accepted Answer

The answer of Determine whether the graph is a tree....

Question 15

Read the poem in the News Clip.  a. If a right-handed mitten is turned inside out, as is suggested in the poem, will it still fit a right hand? b. Is a right-handed mitten topologically equivalent to a left-handed mitten?

Accepted Answer

The answer of Read the poem in the News Clip....

Question 16

Determine whether each of the points A, B, and C is inside or outside of the simple closed curve.
​  1. Point C
2. Point A
3. Point B
a. outside
b. inside
​
-A

Accepted Answer

The answer of Determine whether each of the points A,...

Question 17

Determine whether each of the points A, B, and C is inside or outside of the simple closed curve.
​  1. Point C
2. Point A
3. Point B
a. outside
b. inside
​
-B

Accepted Answer

The answer of Determine whether each of the points A,...

Question 18

Group the objects into classes so that all the elements within each class are topologically equivalent and no elements from different classes are topologically equivalent.

Accepted Answer

Objects A, B, and D are topologically equivalent because they all have the same number of holes, while object C has a different number of holes. Therefore, grouping A, B, and D into one class and C into another class makes the most sense. Within the class of A, B, and D, they cannot be further grouped as they have the same number of holes and same genus. Therefore, the answer is B: A; B and D; C.

Question 19

Is this figure tessellation?

Accepted Answer

The given figure cannot be tessellated because it has curves and irregular edges which cannot fit together without gaps or overlaps. Therefore, it cannot cover a plane without leaving any gaps.

Question 20

Determine whether each of the points A, B, and C is inside or outside of the simple closed curve.

Accepted Answer

The answer of Determine whether each of the points A,...

Quiz 8: The Nature of Measurement

Group the objects into classes so that all the elements within each class are topologically equivalent and no elements from different classes are topologically equivalent. A. a glass B. a bowling ball C. a sheet of typing paper D. a ruler E. a sphere

Let X be a point obviously outside the figure. Draw . How many times does it cross the curve?

Group the objects into classes so that all the elements within each class are topologically equivalent and no elements from different classes are topologically equivalent.

Group the figures into classes so that all the elements within each class are topologically equivalent, and no elements from different classes are topologically equivalent.

Let X be a point obviously outside the figure. Draw . How many times does it cross the curve? It will cross the curve an __________ (even, odd) number of times.

Group the figures into classes so that all the elements within each class are topologically equivalent, and no elements from different classes are topologically equivalent.

Group the objects into classes so that all the elements within each class are topologically equivalent and no elements from different classes are topologically equivalent. A. a bolt B. a brick C. a horseshoe D. a pencil

Determine whether each of the points A, B, and C is inside or outside of the simple closed curve. 1. Point C 2. Point A 3. Point B a. outside b. inside -C

Group the objects into classes so that all the elements within each class are topologically equivalent and no elements from different classes are topologically equivalent. A) a bolt B) a straw C) a sewing needle D) a funnel with a handle

Group the objects into classes so that all the elements within each class are topologically equivalent and no elements from different classes are topologically equivalent. A) a glass B) a bowling ball C) a sheet of typing paper D) a sheet of two-ring-binder paper E) a sphere

Let X be a point obviously outside the figure. Draw . How many times does it cross the curve?

Let X be a point obviously outside the figure. Draw . How many times does it cross the curve? It will cross the curve an __________ (even, odd) number of times.

Read the poem in the News Clip. Is a right-handed mitten topologically equivalent to a left-handed mitten? Answer yes or no. If a right-handed mitten is turned inside out, as is suggested in the poem, will it still fit a right hand? Answer yes or no.

Determine whether the graph is a tree.

Read the poem in the News Clip. a. If a right-handed mitten is turned inside out, as is suggested in the poem, will it still fit a right hand? b. Is a right-handed mitten topologically equivalent to a left-handed mitten?

Determine whether each of the points A, B, and C is inside or outside of the simple closed curve. 1. Point C 2. Point A 3. Point B a. outside b. inside -A

Determine whether each of the points A, B, and C is inside or outside of the simple closed curve. 1. Point C 2. Point A 3. Point B a. outside b. inside -B

Group the objects into classes so that all the elements within each class are topologically equivalent and no elements from different classes are topologically equivalent.

Is this figure tessellation?

Determine whether each of the points A, B, and C is inside or outside of the simple closed curve.

Quiz 8: The Nature of Measurement

Group the objects into classes so that all the elements within each class are topologically equivalent and no elements from different classes are topologically equivalent. A. a glass B. a bowling ball C. a sheet of typing paper D. a ruler E. a sphere

Let X be a point obviously outside the figure. Draw . How many times does it cross the curve? ​ ​

Group the objects into classes so that all the elements within each class are topologically equivalent and no elements from different classes are topologically equivalent.

Group the figures into classes so that all the elements within each class are topologically equivalent, and no elements from different classes are topologically equivalent.

Let X be a point obviously outside the figure. Draw . How many times does it cross the curve? ​ ​ It will cross the curve an __________ (even, odd) number of times.

Group the figures into classes so that all the elements within each class are topologically equivalent, and no elements from different classes are topologically equivalent.

Group the objects into classes so that all the elements within each class are topologically equivalent and no elements from different classes are topologically equivalent. A. a bolt B. a brick C. a horseshoe D. a pencil

Determine whether each of the points A, B, and C is inside or outside of the simple closed curve. ​ 1. Point C 2. Point A 3. Point B a. outside b. inside ​ -C

Group the objects into classes so that all the elements within each class are topologically equivalent and no elements from different classes are topologically equivalent. A) a bolt B) a straw C) a sewing needle D) a funnel with a handle

Group the objects into classes so that all the elements within each class are topologically equivalent and no elements from different classes are topologically equivalent. A) a glass B) a bowling ball C) a sheet of typing paper D) a sheet of two-ring-binder paper E) a sphere

Let X be a point obviously outside the figure. Draw . How many times does it cross the curve? ​ ​

Let ​X be a point obviously outside the figure. Draw . How many times does it cross the curve? ​ ​ It will cross the curve an __________ (even, odd) number of times.

Read the poem in the News Clip. Is a right-handed mitten topologically equivalent to a left-handed mitten? Answer yes or no. If a right-handed mitten is turned inside out, as is suggested in the poem, will it still fit a right hand? Answer yes or no.

Determine whether the graph is a tree.

Read the poem in the News Clip. a. If a right-handed mitten is turned inside out, as is suggested in the poem, will it still fit a right hand? b. Is a right-handed mitten topologically equivalent to a left-handed mitten?

Determine whether each of the points A, B, and C is inside or outside of the simple closed curve. ​ 1. Point C 2. Point A 3. Point B a. outside b. inside ​ -A

Determine whether each of the points A, B, and C is inside or outside of the simple closed curve. ​ 1. Point C 2. Point A 3. Point B a. outside b. inside ​ -B

Group the objects into classes so that all the elements within each class are topologically equivalent and no elements from different classes are topologically equivalent.

Is this figure tessellation?

Determine whether each of the points A, B, and C is inside or outside of the simple closed curve.

Let X be a point obviously outside the figure. Draw . How many times does it cross the curve?

Let X be a point obviously outside the figure. Draw . How many times does it cross the curve? It will cross the curve an __________ (even, odd) number of times.

Determine whether each of the points A, B, and C is inside or outside of the simple closed curve. 1. Point C 2. Point A 3. Point B a. outside b. inside -C

Let X be a point obviously outside the figure. Draw . How many times does it cross the curve?

Let X be a point obviously outside the figure. Draw . How many times does it cross the curve? It will cross the curve an __________ (even, odd) number of times.

Determine whether each of the points A, B, and C is inside or outside of the simple closed curve. 1. Point C 2. Point A 3. Point B a. outside b. inside -A

Determine whether each of the points A, B, and C is inside or outside of the simple closed curve. 1. Point C 2. Point A 3. Point B a. outside b. inside -B