Math Forum / Mathematics / Recreational Math / November 2008

From "Teaching Mathematics:  A Sourcebook of Aids, Activities, and
Strategies" (page 28), the following pattern puzzle is presented (and
note that the asterisk is not given its normal meaning of
multiplication and the arrow siglum does not necessarily mean equal

I am an engineering student with a simple geometric relationship
question I was hoping someone might be able to assist with. I've made
a dodgy sketch of it available at:
http://img162.imageshack.us/my.php?image=dryergeometryproblemyb8.jpg

Considering the sides a, b, c of an arbitrary triangle as coordinates of a point in the 3D space, determine the region in 3D space that represents all possible triangles.
Best regards,
   Avni

Let a, b, c, d, e, f be the sides of an orthocentric tetrahedron, such that d is opposite to a, e to b, f to c, and
d = sqrt((2*b^2+2*c^2-a^2)/3) ,
e = sqrt((2*c^2+2*a^2-b^2)/3) ,
f = sqrt((2*a^2+2*b^2-c^2)/3) .

You are familiar with the proof that Sigma (1/x(x+1)) from 1 to
infinity equals 1, by writing 1/x(x+1) as 1/x - 1/(x+1) so we have
Sigma (1/x - 1/(x+1)) = 1/1 + 1/2 + 1/3+... - (1/2 + 1/3+...) and all
but the first term cancels so we have it equal to 1.

Here's a problem with roots in my middle school math
teacher past.
Imagine a school with m students in each grade level,
where each grade level is divided into n classes.

The ten digits 0-9 can be arranged 3 628 800 differet ways without
repeating any digit.per set of ten.
These are not equally random.. Compare 0-1-2-3-4-5-6-7-8-9- with
0-9-1-8-2-7-3-6-4-5  and look at the gaps.

Do you suffer from a tough class? Are you looking for instructor
solutions manual to do your homework? Just send me email with its name
and edition and I may be able to help you in low price! It is my list,
however if you don't find it here don't give up because it is only a

Consider the following simple abstraction of the game of Poker.
There are two players. At the start of the game, each player puts one
chip into the pot. The dealer deals each player a random real number
chosen from the interval [0, 1], using the uniform distribution. You can

In my previous post about a 10x10 matrix I asked how to construct a
'random' matrix and was a sked for my definition of random. I now
might have an idea about measuring its randomness.
Start with a random line of all ten digits and then repeat them on the

An ordered 10x10 matrix with all digits is easy to generate with paper
and pencil by starting with the line 0-1-2-3-4-5-6-78-8-9 and then
shifting this line one step to write the next 1-2-3-4-5-6-7-8-9-0 and
so on till all 10x10 lines and verticals have been drawn so that  all

There has been an animated discussion at rec.gambling.lottery about
how many sets of five pairs can be generated from ten digits in an urn
if you draw two at  a time without replacement, so that each set has
all ten digits.

Check out this useful website for Math, you can download e-worksheets
or can virtually practice Math online.  Visit www.mathebook.net
You will find Addition / subtraction / division / even odd numbers,
Roots & Square number,  Algebra, Geometry, Trigonometry, Missing

Have you come up with any interesing math facts that would be a good
addition to www.odd-info.com ?

Just for fun:
Let S_n be the sum of n's digits.  Show that
   S_1 z + S_2 z^2 + S_3 z^3 + ...
has |z| = 1 as its natural boundary.