Things I find Interesting
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.
- The Discarded Digit
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
- 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
- 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
Click here if you
want the timeline in its own window.
- 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
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
- I wrote a paper for the Math Monthly many years ago about
projecting a quadrangle into a parallelogram. In the process of
solving this problem, I discovered how to project the quadrangle
into a rectangle. It then appeared that it was possible that the
quadrangle could be projected into a square. Over the years I
would periodically think about this, but I never did find the
point(s) at which the projection would yield a square. The
figures in this paper were done using Geometers Sketchpad. If
you are interested in this problem, then click here to read about how
a quadrangle can be projected into a parallelogram.
- Try the Mind
Reader. The computer will read your mind.
- 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
- 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)=
2p - 1*(2p - 1).
- 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
- 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
- The sole cause of all human misery is the inability of people
to sit quietly in their rooms.
- If I cannot brag of knowing something, then I brag of not
- The perplexity of life arises from there being too many
interesting things in it for us to be interested properly in any
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
- 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
- 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.