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Direct linkOsler, Thomas J. – International Journal of Mathematical Education in Science and Technology, 2010
"Lord Brouncker's continued fraction for pi" is a well-known result. In this article, we show that Brouncker found not only this one continued fraction, but an entire infinite sequence of related continued fractions for pi. These were recorded in the "Arithmetica Infinitorum" by John Wallis, but appear to have been ignored and forgotten by modern…
Descriptors: Mathematics Instruction, Mathematical Concepts, Equations (Mathematics), Mathematical Formulas
Osler, Thomas J. – International Journal of Mathematical Education in Science & Technology, 2006
Euler gave a simple method for showing that [zeta](2)=1/1[superscript 2] + 1/2[superscript 2] + 1/3[superscript 2] + ... = [pi][superscript 2]/6. He generalized his method so as to find [zeta](4), [zeta](6), [zeta](8),.... His computations became increasingly more complex as the arguments increased. In this note we show a different generalization…
Descriptors: Mathematics Education, Mathematical Concepts, College Mathematics, Computation
