The number pi contains all ten digits in its decimal form as does e, sqrt(2) and most familiar irrationals. It is more difficult to find relatively simple fractions that contain all ten digits. It is somewhat surprising that nearly all real numbers contain all ten digits. Attached is a “proof” of that result. This discussion…
Here is a sketch and some math to demonstrate that it is possible to connect four towns on the corners of a one mile by one mile square with only 1 + Sqrt(3) miles of wiring. I believe that this is the minimum possible. Click below on “FourPts” to see the work. FourPts
Using the square root function infinitely many times will change any positive number to one. That is to say the limit will be one. Attached is an example of reducing 8 to one using lots of square roots. InfSqrt2
Here are some of my notes produced as I searched for integer solutions to: A^2 – 3(B^2) = 13 Click below to see my work. Do you see a pattern? DiophSq13
I have taught at more than one high school and am familiar with others which rank their senior class using a method that makes me cringe at the errors that are produced. In both math and science courses we teach the importance of using significant digits in calculating results. In establishing a numerical grade teachers…
While pondering different orders of infinity and how to map one infinite set of real numbers onto another infinite set of real numbers, I displayed the following symptoms of a mental breakdown! Click below to see my scribbles on this peculiar function. ChampEmbed2
Here is a bit of work with a type of infinite continued fraction. Click ContdFrac below to see my work ContdFrac
There are still a few missing numbers in the 2017 puzzle. Click below to see the progress so far. The rules are that the digits 2 0 1 7 have to be in their original order. Common mathematical symbols and grouping may be inserted to attempt to get the desired result. Click on 2017pdf below…