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Tag: Conic sections
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Making the Case We are in the middle of a series of posts on conic sections. After the introductory post, Finding Refreshment in the Desert, I devoted three posts to the circle and two each to the parabola, ellipse, and hyperbola. In the previous post I had mentioned a degenerate conic section known as a pair…
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The Riddle of the Name In this post we continue with our study of the conic sections. So far we have looked at the circle, the parabola, and the ellipse. Now we turn to the final non-degenerate conic section – the hyperbola. When we hear the word ‘hyperbola’, some of us may think of the…
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Brief Recapitulation In this post we continue with the series on conic sections. In the previous post, A Mathematical Shortfall, we introduced the ellipse and derived the equation of the ellipse in standard form. We also obtained the equation for the auxiliary circle of the ellipse and the equation of the tangent at a point…
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The Riddle of the Name When I was in school, one of my English teachers (unfortunately I do not recall which one) taught us about the punctuation mark known as the ellipsis. An ellipsis is three dots (…) that indicate something is missing. It could a lack of words, such as…, well…, you see…, indicating…
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Brief Recapitulation In the previous post, titled Mathematical Parables, I introduced us to the parabola. Just to jog your memory, a conic section is a a geometric figure such that, for any point on the conic section, the ratio of its distance from a fixed point, called the focus, to its distance from a fixed…
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Starting the Parabolic Path Those who know me well, know that I have two main areas of interest. Since you are reading this blog, you probably know or have surmised that mathematics is one of those areas. If you do not yet know, the other area is the exploration of my Christian faith and to…
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Brief Recapitulation We are in the middle of a series of posts on conic sections. In the previous post, we derived the equation of a circle centered at the origin and having a radius of r. We also derived the equation of the tangent at a point on the circle. To jog your memory, given…
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Defining a Circle Three weeks back, I started a series on conic sections. I did not post the last two weeks due to being ill. We continue today with a study of the first conic section – the circle. Just as a reminder about conic sections, take a look at the figure below. As is…
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A Forty Year Fascination I was in the eleventh grade when I was introduced to a part of analytical geometry (or coordinate geometry, if you wish) that would fascinate me over the years. Don’t get me wrong. When I first learned about this aspect of analytical geometry, which is now almost forty years ago, I…
Acutely Obtuse 