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Math Help - Geometric Proofs?

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    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!
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  2. #2
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    Quote Originally Posted by Samson View Post
    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.
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    Quote Originally Posted by undefined View Post
    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.
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    Quote Originally Posted by Samson View Post
    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.
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    Quote Originally Posted by undefined View Post
    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?
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