Thread: Geometric Proofs?

Hello All, I was covering the topic of Geometric Proofs in my text today and I have a few questions.

Q1: Suppose there is a line L. Using a geometric proof, the slope of L denoted as 'm' can be estimated in terms of a slope point P whose coordinates are (x,y). This proof will consider the case of the point P being located above L. Can somebody prove this?

Q2: A method exists which constructs a sequence of non-negative integers (a_0, a_1, a_2, a_3, ...). This method also details that a_n is strictly positive for positive n. However, an example exists for which a_0 may be zero. Can anyone think of an example and explain its geometric significance?

Essentially I need to specify a a_n for which a_0 = 0 .

Any help is appreciated!

Originally Posted by Samson

Hello All, I was covering the topic of Geometric Proofs in my text today and I have a few questions.

Q1: Suppose there is a line L. Using a geometric proof, the slope of L denoted as 'm' can be estimated in terms of a slope point P whose coordinates are (x,y). This proof will consider the case of the point P being located above L. Can somebody prove this?

Q2: A method exists which constructs a sequence of non-negative integers (a_0, a_1, a_2, a_3, ...). This method also details that a_n is strictly positive for positive n. However, an example exists for which a_0 may be zero. Can anyone think of an example and explain its geometric significance?

Essentially I need to specify a a_n for which a_0 = 0 .

Any help is appreciated!

There isn't enough information for either Q1 or Q2 to tell what you're talking about. Why are we estimating the slope of a line? What does this sequence represent? Please provide more context.

Originally Posted by undefined

There isn't enough information for either Q1 or Q2 to tell what you're talking about. Why are we estimating the slope of a line? What does this sequence represent? Please provide more context.

I'm not really sure why we are estimating the slow of a line, but I assume the only reason is because it asks us to! I don't know the purpose in it! The question is vague but it should be solvable.

As far as the second question, I'm not sure what it represents either. I do know what the latter part of the question is asking, and I think it is just relating it to the set of numbers previously mentioned.

Originally Posted by Samson

I'm not really sure why we are estimating the slow of a line, but I assume the only reason is because it asks us to! I don't know the purpose in it! The question is vague but it should be solvable.

As far as the second question, I'm not sure what it represents either. I do know what the latter part of the question is asking, and I think it is just relating it to the set of numbers previously mentioned.

Hmm I can't make any sense of it. Q1: We're asked to prove that it is possible to approximate the slope of a line using a nearby value? Huh?? Q2: We're asked to construct a sequence, where all we know is a_0 = 0, and a_i > 0 for i > 0. So, just use a_i = i. These points lie along the line y = x, graphically. Meaning? None because there is no context given.

Originally Posted by undefined

Hmm I can't make any sense of it. Q1: We're asked to prove that it is possible to approximate the slope of a line using a nearby value? Huh?? Q2: We're asked to construct a sequence, where all we know is a_0 = 0, and a_i > 0 for i > 0. So, just use a_i = i. These points lie along the line y = x, graphically. Meaning? None because there is no context given.

I agree that the context is poor. Does anyone else have any other ideas what they could be saying here in case we're missing something?