mixedmath

Explorations in math and programming
David Lowry-Duda



While idly thinking while heading back from the office, and then more later while thinking after dinner with my academic little brother Alex Walker and my future academic little sister-in-law Sara Schulz, we began to think about $2017$, the number.

General Patterns

Counting to 20

$$\begin{array}{ll} 1 = 2\cdot 0 + 1^7 & 11 = 2 + 0! + 1 + 7 \\ 2 = 2 + 0 \cdot 1 \cdot 7 & 12 = 20 - 1 - 7 = -2 + (0! + 1)\cdot 7 \\ 3 = (20 + 1)/7 = 20 - 17 & 13 = 20 - 1 \cdot 7 \\ 4 = -2 + 0 - 1 + 7 & 14 = 20 - (-1 + 7) \\ 5 = -2 + 0\cdot 1 + 7 & 15 = -2 + 0 + 17 \\ 6 = -2 + 0 + 1 + 7 & 16 = -(2^0) + 17 \\ 7 = 2^0 - 1 + 7 & 17 = 2\cdot 0 + 17 \\ 8 = 2 + 0 - 1 + 7 & 18 = 2^0 + 17 \\ 9 = 2 + 0\cdot 1 + 7 & 19 = 2\cdot 0! + 17 \\ 10 = 2 + 0 + 1 + 7 & 20 = 2 + 0! + 17. \end{array}$$

In each expression, the digits $2, 0, 1, 7$ appear, in order, with basic mathematical symbols. I wonder what the first number is that can't be nicely expressed (subjectively, of course)?

Iterative Maps on 2017

Now let's look at less-common manipulations with numbers.

A Few Matrices


Leave a comment

Info on how to comment

To make a comment, please send an email using the button below. Your email address won't be shared (unless you include it in the body of your comment). If you don't want your real name to be used next to your comment, please specify the name you would like to use. If you want your name to link to a particular url, include that as well.

bold, italics, and plain text are allowed in comments. A reasonable subset of markdown is supported, including lists, links, and fenced code blocks. In addition, math can be formatted using $(inline math)$ or $$(your display equation)$$.

Please use plaintext email when commenting. See Plaintext Email and Comments on this site for more. Note also that comments are expected to be open, considerate, and respectful.

Comment via email

Comments (1)
  1. 2017-01-22 engin

    Sounds like a cricket match between Hardy and Ramanujan.