course Mth 151
6/20 10
Question: `q001. Note that there are 7 questions in this assignment.
Sketch three points A, B and C forming an equilateral triangle on a piece of paper, with point A at the lower left-hand corner, point B at the lower right-hand corner and point C at the top. Sketch the segments AB and AC.
Now double the lengths of AB and AC, and place a point at each of the endpoints of these segments. Connect these new endpoints to form a new equilateral triangle. Two sides of this triangle will have three points marked while the new side will only have its two endpoints marked. Fix that by marking that middle point, so all three sides of your new triangle are marked the same.
How many marked points were there in the original triangle, and how many are there in the new triangle?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
There were 3 marked points in the original triangle and then when the triangle was extended 2 more end points were marked and then the middle of the third side was marked to make 6 points on the new triangle.
3
Ok
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Question: `q002. Extend the two sides that meet at A by distances equal to the original lengths AC and AB and mark the endpoints of the newly extended segments. Each of the newly extended sides will have 4 marked points. Now connect the new endpoints to form a new right triangle. Mark points along the new side at the same intervals that occur on the other two sides. How many marked points are on your new triangle, and how many in the whole figure?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
There were 6 points on the triangle before the sides were extended again. When they are extended there are now 10 marked points once the new side has been marked at the same intervals as the other two sides.
3
Ok
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Question: `q003. Continue the process for another step-extend each side by a distance equal to the original point-to-point distance. How many points do you have in the new triangle?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
By extending the two sides an equal distance again we have 13 end points before adding the new points inside the new, larger triangle which gives us a total of 15 marked points.
3
Ok
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Question: `q004. Continue the process for one more step. How many points do you have in the new triangle?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
By extending the two sides another equal distance we will have the 15 old points plus the 6 new points on the extended side for a total of 21 marked points.
3
Ok
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Question: `q005. The sequence of marked points is 3, 6, 10, 15, 21. What do expect will be the next number in this sequence?
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Your solution:
The differences in the numbers in the sequence are 3, 4, 5, 6. Since the next difference is 7 the next number in the sequence is 28.
3
Ok
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Question: `q006. How can you tell, in terms of the process you used to construct these triangles, that the next number should be 7 greater?
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Your solution:
Imagining the triangle being extended there will be two new endpoints added for a total of 7 points.
3
Ok
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Question: `q007. How do you know this sequence will continue in this manner?
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Your solution:
Every time the triangle is extended the side is increased by one and all of the new points are on the new side so the total number of points would increase by one more than the previous extension.
3
Ok
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