Stretching Space

  • Calvin C. Clawson


In previous chapters we introduced Fermat’s and Descartes’ splendid rectilinear coordinate system, which allows us to graph various symbolic relationships. However, we can’t stop with just the simple Cartesian system, for the curious cannot leave well enough alone. We must see if it is possible to alter the rectilinear coordinate system into something even more interesting. For example, what happens when we use a y-axis that is not perpendicular to the x-axis? Figure 92 shows such a system where the y-axis intersects the x-axis at 60 degrees. In the second quadrant we have drawn a normal circle whose equation is:
$$ {(x + 4)^2} + {(y - 4)^2} = 4 $$


Matrix Algebra Infinite Series Transformation Equation Original Matrix Logarithmic Spiral 
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  1. 1.
    Carl Boyer, A History of Mathematics (New York: John Wiley and Sons, 1991), p. 448.MATHGoogle Scholar
  2. 2.
    Ibid., p. 458.Google Scholar
  3. 3.
    Eli Maor, e: The Story of a Number (Princeton, New Jersey: Princeton University Press, 1994), p. 123.MATHGoogle Scholar
  4. 4.
    Some may object to this characterization of Cambridge University. However, when we think of English mathematicians, we think of Wallis, Barrow, Newton, Cayley, Sylvester, Littlewood, Hardy, Russell, and Ramanujan—all Cambridge boys.Google Scholar
  5. 5.
    Boyer, A History of Mathematics, p. 586.Google Scholar
  6. 6.
    Ibid., p. 588.Google Scholar
  7. 7.
    Ibid., p. 520.Google Scholar
  8. 8.
    Ibid., p. 546.Google Scholar
  9. 9.
    Lloyd Motz and Jefferson Hane Weaver, The Story of Mathematics (New York: Plenum Press, 1993), p. 282.Google Scholar
  10. 10.
    Ibid., p. 285.Google Scholar

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© Calvin C. Clawson 1999

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  • Calvin C. Clawson

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