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between the conic sections. These ideas led to other concepts of continuity. For instance, if a circle and a straight line were two expressions of the same shape, perhaps a line could be thought of as a circle of infinite
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The basic idea behind geometric continuity was that the five conic sections were really five different versions of the same shape. An
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to be identical. Such ideas were useful in crafting the modern, algebraically defined, idea of the
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182:. For such to be the case, one would have to make the line closed by allowing the point
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333:. Vol. 11 (11th ed.). Cambridge University Press. pp. 674–675.
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as the eccentricity drops toward one; it can also tend to intersecting
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126:(and related shapes) by mathematicians such as
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320:"Geometrical Continuity"
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259:{\displaystyle x=-\infty }
230:{\displaystyle x=+\infty }
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283:{\displaystyle \infty }
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294:for more).
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140:continuity
107:April 2024
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278:∞
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317:(1911).
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