MATC Mathematics Club
Madison Area Technical College
Professor aBa Mbirika, Eau Claire
"Pi is Transcendental"
One of the most famous mathematical formulas is Euler’s relation e to the power i pi plus 1 equals 0. Its beauty lies in the simplicity in which it puts together the transcendental numbers e and pi, the imaginary number i, the constants 0 and 1, and the operations of exponentiation, multiplication and addition. But what is meant by the term “transcendental number”? In this talk, we briefly survey transcendental numbers and explore where they sit in the terrain of the irrational numbers. We also remark on the various types of infinities (the countable and the uncountable) and how the transcendental numbers are of a “bigger infinity” than that of their infinite counterpart, the algebraic numbers. Finally, we focus on some neat properties of the famous transcendental number, pi. And we explore how the proof of the transcendence of pi back in 1882 helped to prevent the Indiana House of Representatives in 1897 from passing a bill decreeing the exact value of pi to be 3.2—yes, this almost happened.
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