Things I find Interesting
and
Other Odds and Ends

This page will contain a variety of things. Usually what will appear on this page will be of a mathematical nature. There may be historical notes of interest, there may be mathematical puzzles, or there may appear quotations I find interesting or amusing.

Here is a little challenge. The computer will ask you to choose any number base from three to ten. Then you will choose any number in that base of three or more digits. Now using the same digits you used to make the original number make another number. You will then subtract the smaller of the two numbers from the larger (in your chosen base). Once this operation is completed, you will discard one of the non-zero digits. You will then enter the number obtained by removing a digit. You will then be told what digit you discarded. How is it done? Play Knowing the Discarded Digit

• Fifty-three years ago, when I was an undergraduate student taking a geometry course, Professor Cook gave a short lecture on the orthic triangle and some of its properties. Now, fifty-three years later, I rediscovered the orthic triangle in a round-about way. One of the things that keeps me excited about mathematics is the fact that I can be looking at something that eventually leads me on an adventure that ends in a new discovery or a rediscovery of something I had long ago forgotten. I just went on such an adventure and if you would like to share my discovery of the orthic triangle just click here.
• I am currently working on a Math-History timeline for use by my students and other interested parties. It is a two column listing with mathematics related events on the left and historical events on the right. The selections are mine (many selected from the timeline given in A History of Mathematics by Carl Boyer) and are not intended to be all-inclusive. Events that are in a grey box will pop up a brief paragraph about the event when your mouse hovers over it. These are indeed brief and are intended to spur the reader's interest to seek out further information about the person or event. Often individual mathematicians are introduced by something they wrote or did. This is a constantly changing page as I am working on it all the time -- it is my summer project for the hot hours of the day. I would appreciate any feed back concerning errors or general comments. The link is Math-History Timeline

• Some Subsequences of the Fibonacci Sequence. Several years ago I stumbled upon an interesting recurrence relation that generated terms of the Fibonacci sequence. I later discovered a collection of similar recurrence relations. In the attached note, I develop this collection of sequences each of which is a subsequence of the Fibonacci sequence. Each of these sequences has the property that the quotient of consecutive terms converges to a power of the golden ratio. The sequences that are defined involve Fibonacci and Lucas numbers in their definitions.
A PDF file of this note can be downloaded here. Subsequences of the Fibonacci Sequence.

• I have a history page at http://www.math.wichita.edu/history that is listed in my links as the Math 750J page. This is material produced by students in two summer work-shops on the history of mathematics for middle school teachers. The page contains biographies of men and women who have made contributions to mathematics, some topics in mathematics and some classroom activities. I have been asked to put a link here to make it more accessible.

• I wrote some notes about Super Heronian Triangles after I talked about them in a recent class. Later a student requested I put the information on my web page so he could give a friend the URL. So if you are interested in triangles whose sides are three consecutive integers and whose area is also an integer, then click here to read about them.

• I was at a meeting with some colleagues where one of my colleagues posed the following problem:

A steel company has developed the ability to make railrod track in straight one-mile sections. The Huff-and-Puff railroad needs to replace a section of straight track that is exactly one mile long. Two one-mile sections of rail are ordered; however an error is made and one of the rails is exactly one foot too long. When the workers laid the track and discovered that one rail was a foot too long, they decided to squeeze it in anyway. If, when they squeezed it in, the rail formed a perfect arc of a circle, how far out of line is it at the widest point?

That is, in the figure below, we wish to determine h.

What would you guess the distance to be? After you think about it for a while, you can go here for a solution.

• I am working on a mathematics notebook in which I will put the mathematical things I have been working on. This will always be under construction.

• You have got to see this to believe it. Ben Franklin's Magic Square. This is a 16x16 magic square with phenomenal properties.

• Here is a page devoted to material related to the PythagoreanTheorem and related topics.

• Here is a page devoted to the cycloid. It is not completed but the animated gif is fun to watch.

• On February 18, 2005,  Dr. Martin Nowak (from Germany) found the 42th known Mersenne prime 225,964,951-1.

• Two in one year! On December 15, 2005, two professors at Central Missouri State University, Drs. Curtis Cooper and Steven Boone, discovered the 43rd Mersenne prime, 230,402,457 - 1. This  prime is 9,152,052 digits long. This prime now yields the 43rd perfect number.

• They did it again!  The group from Central Missouri State University, Drs. Curtis Cooper and Steven Boone, discovered the 44th Mersenne prime, 232,582,657 - 1 on September 4, 2006. This new prime is 9,808,358 digits long. Still short (but, Oh, so close!) of the illusive 10 million digit prime that will win the finders \$100,000 from the Electronic Frontier Foundation.

• I've been lax in keeping this page up. On August 23, 2008 the 45th known Mersenne prime was discovered by Edson Smith. 243112609 - 1 is the largest known prime number with 12,978,189 digits!

• The 46th known Mersenne prime, 237156667 - 1, was discovered by Hans-Michael Elvenich on September 6, 2008

• On April 12, 2009, Odd Magnar Strindmo discovered the 47th known Mersenne prime, 242643801 - 1. This prime now yields the 47th known perfect number.

• On January 25th, 2013  Dr. Curtis Cooper discovered the 48th known Mersenne prime, 257,885,161-1, a 17,425,170 digit number. This find shatters the previous record prime number of 12,978,189 digits, also a GIMPS prime, discovered over 4 years ago.

• Again, I've been lax in keeping this page up. On January 7, 2016 Dr. Curtis Cooper discovered the 49th known Mersenne prime, 274207281-1, a 22,338,618 digit number.

• The 49 known perfect numbers (as of April 2017) can be computed using the following values in the formula where the prime p = 2p-1, where p comes fom the table below. For example, the first perfect number is 2*(22 -1) = 2*3=6 and the third perfect number is 24(25-1)= 16*31=496.
2p - 1*(2p - 1).
•  2 3 5 7 13 17 19 31 61 89 107 127 521 607 1279 2203 2281 3217 4253 4423 9689 9941 11213 19937 21701 23209 44497 86243 110503 132049 216091 756839 859433 1257787 1398269 2976221 3021377 6972593 13466917 20996011 24036583 25964951 30402457 32582657 37156667 42643801 43112609 57885161 74207281

• A little humor.
 A tech ed teacher, a math teacher and a physics teacher were standing around a flagpole when an English teacher wandered by. "What are you doing ?" she asked. "We need to know the height of the flagpole," answered one, "and we're discussing the formula we might use to calculate it." "Watch!" said the English teacher. She pulled the pole from its fitting, laid it on the grass, borrowed a tape measure and said, "Exactly 24 feet." Then she replaced the pole and walked away. "English teacher!" sneered the math teacher. "We ask for the height, and she finds the length."

• A great thought.
 The mathematician does not study pure mathematics because it is useful; he studies it because he delights in it and he delights in it because it is beautiful. Poincaré

• Another great thought.
 What you have been obliged to discover by yourself leaves a path in your mind which you can use again when the need arises. George Christoph Lichtenberg (1742-1799)

• The sole cause of all human misery is the inability of people to sit quietly in their rooms.
Blaise Pascal, 1670

• If I cannot brag of knowing something, then I brag of not knowing it.
R. W.Emerson, 1866

• The perplexity of life arises from there being too many interesting things in it for us to be interested properly in any of them.
G. K. Chesterton, 1909

• Here is a little puzzle. A secretary finds that she has an extraordinary social security number.Its nine digits contain all the numbers from 1 through 9. They also form a number with the following characteristics: when read from left to right,its first two digits form a number divisible by 2, its first three digits form a number divisible by 3, its first four digits form a number divisible by 4, and so on, until the complete number is divisible by 9. What is the secretary's social security number?

If you enjoy mathematical problems and puzzles, try the problem page.This page contains a collection of problems and puzzlers I have used in the past for our Math Awareness Problem Competition.

• Scientists have long been concerned with the problem of how wind and temperature effect the human body. On November 1, 2001 a new formula for computing the wind chill factor was introduced. Click here for the new Wind Chill Factor Chart with some information on how the values are determined mathematically. Click here for the old Wind Chill Factor Chart with some information on how its values were determined mathematically.

• Here is a Heat Index Chart with some information on how the values are determined mathematically.

• Here is some information on earthquakes with some information on how the power of an earthquake in released energy is related to the magnitude, as given by the Richter scale.

• Some things for calculus students. Animation of the cycloid, Animation of the polar graph r = cos 2θ ,Animation of the polar graph r = 1 + 2cos θ, also Animation of the polar graph r = sin θ+ sin3(5θ/2).

Updated 10 October 2014.