DescriptionA "palindrome" is a word, sentence, or set of sentences that spell the same backwards as forwards. Numbers can also be palindromes; examples are 22, 313, 4554, 89098, 2277722, and so on. Often, one can take a non-palindromic number and create a palindromic one from it by reversing the digits, adding the result to the original number, and iterating this procedure until a palindrome is found. All numbers less than 10,000 will produce a palindrome in this way, with one bizarre exception, the number 196!Transcendental numbers are numbers which are irrational, but not a solution to a polynomial equation with rational coefficients. Examples are ``pi'' and the base of the natural logarithm ``e''. Many of these numbers are famous for the ingenuity that was required to prove their transcendentality. The Hardy-Ramanujan number 1729 is the smallest number expressible as the sum of cubes in two different ways: 13 + 123 or 93 + 103. This intriguing property was discovered by Ramanujan after Hardy mentioned that ``1729 is rather a dull number for a London taxi''. Generalisations of such numbers are known as taxicab numbers and have various interesting connections to other special numbers, e.g. Ramanujan doubles. In this project, you will analyse one of these special types of numbers, or explore other numbers with special properties.
PrerequisitesLinear Algebra and Analysis in Many VariablesResources and referencesFor some reading see: Zoo of numbers, World of numbers, Taxicab numbers and Palindromic numbers at MathWorld. |
email: Marija Zamaklar