“Integrating” Creativity and Technology Through Interpolation
The digital age of the 21st century is ubiquitous with easy access to information. Students of mathematics find at their fingertips (literally) immense resources such as Wolfram Math and other digital repositories where anything can be looked up in a few clicks. The purpose of this chapter is to convey to the reader that Mathematics as a discipline offers examples of how hand calculations using first principles can result in deep insights that present students with the opportunities of learning and understanding. By first principles we are referring to fundamental definitions of mathematical concepts that enable one to derive results (e.g., definition of a derivative; definition of a Taylor series etc.). We also highlight the value of integrating (pun intended) technology to understand functions that were obtained via mathematical interpolation by the likes of John Wallis (1616–1703), Lord Brouncker (1620–1684), Johann Lambert (1728–1777) and Edward Wright (1558–1615). The interpolation techniques used by these eminent mathematicians reveals their creativity in deriving representations for functions without the aid of modern technology. Their techniques are contrasted with modern graphing techniques for the same functions.
KeywordsCircular functions Π John wallis Quadratures (areas) Conformal maps Secant function Integration History of calculus History of infinite series Interpolation Mathematical creativity
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