4.669............like the 5th level of P's triangle..........6.5..............the midpoint of 2 - 11...............can be written as ........13/2.................13/2 = 6.5................midpoint.......halfway through................also the average of those ten numbers............2 - 11...................half way.........midpoint...........like 1/2.........the location.....vertically.......of the critical line..........1331..........is in the 4th level............................6.5 forms a fractal pattern with 65............what the ten numbers.........2 - 11.........sum to....................5 13's.............added beg to end................

65.......................what 3 and 2 sum and produce......................the last two successive pairs of numbers...........whose sum and multiple are but a digit apart..............as 2 and 3 are..........the 1st two primes.....period.....................and as part of a right triangle................gives u a hyp of the square root of 13.................3.60..........like full circle...........like 2 pi....................................

Upside down......2 becomes.....1/2. (2 to the neg 1)............6.5...................is 13/2.................13/2 is the same as 13(1/2).........................1/2...........the critical line.................is also in the 3rd level of P's triangle.......................from either side...............r.s..........connecting East and West ........West and East.................the zeros at all negative even numbers...........so called trivial zeros........not so trival after all.................and the line at 1/2...........in the East............in positive numbers.......negative even numbers as exponents........like the zeros on the X axis..........spin a number..............2 to the neg 2..................................is 1/4................the fractions of the harmonic series........1/2........to the neg 2..................is 4.................b/c it is like spinning 1/2 upside down and squaring it..........neg two...............as an exponent............to a series of fractions..............as in the harmonic series...............spins then and squares them............................(-2, 0)..........the location of the 1st zero...............on the X axis...................is the same as y = x ^2.............to positive intergers..............



Pascal's Triangle

One of the most interesting Number Patterns is Pascal's Triangle (named after Blaise Pascal, a famous French Mathematician and Philosopher).
To build the triangle, start with "1" at the top, then continue placing numbers below it in a triangular pattern.

Each number is the numbers directly above it added together.
(Here I have highlighted that 1+3 = 4)

Patterns Within the Triangle