Even more patterns come out of that.......................taking out the primes........from the simplified fractions............5, 11, 3, 13, 7..................from 5 to 11.....is 6.......from 11 to 3....is 8....like 68%.....the 1st stand dev from the norm.....

68
95
99.............one is in the 60s.....two in the 90s..........9 + 9 = 18.......a truncated pi..........to of them ........one emerges from comparing the 2nd with the 3rd.....like 2 and 3.....the start of all primes........and one from just using the 3rd.......99.....9 + 9 = 18.........67, 71.........89. 97.....two prime pairs......under 100.......whose single digit matches the next primes double digit........9 + 9 = 18....in 89 and 97..............

9/8, 10/8, 11/8, 12/8, 13/8, 14/8, 15/8, 16/8
9/8, 5/4, 11/8, 3/2, 13/8, 7/4, 15/8, 2.....................

0 and 1.....sum to 1....when comparing their sums and products.....the base comes out, 10...........addition is more basic than multiplication.......addition is the most fundamental process in all math...simple summing...............3 and 2.....like 3/2 = 1.5............the 1st 5 primes, the 1st 5 non primes.......from the c line at 1/2 to 2, 0 is a distance of 3/2.......1.5.............12..........is the 1st of all that in double digits....two types of leaps......


0 + 1 = 1
0 * 1 = 0

1 + 2 = 3
1 * 2 = 2

2 + 3 = 5
2 * 3 = 6

3 + 4 = 7
3 * 4 = 12

It is the 4th pair.................like 24.....like 11 + 13 = 24.....like 72/3 = 24...............like 2/4 = 1/2.......3 * 4 = 12.......12 is like 1/2, the c line.................2 + 2 = 4......2 * 2 = 4.....balance and a leap at 4..........for the 4th pair.............a line in the 4th dimension..................

2 - 11............the prime fund...??? One of them......maybe.....sum to 65.......the average is 6.5....patterns.........5 and 6............................

2, 3, 5, 7
2, 4, 6, 8

4, 7, 11, 15.....................break that in half.......4 + 7 = 11.....11 + 15 = 26.....iron.....change in a star......26...........2/6 = 1/3.........1/3 from the harmonic series............................11 + 26 = 37............37 becomes 10......the base.......3 + 7 = 10.............10 is also the sum of the 1st 5 non primes......4, 6.....8. 9. 10..........a 2 and 3...when grouped like that.....set theory.......8, 9 and 10.....sum to 27.......like e

Taking the 1st 5 primes................2, 3........5, 7, 11..............a 2 and 3...pattern...when grouped like that ...AND 5, 7, and 11 sum to 23.........................a right triangle.....whose largest angle is 90.........with sides 2 and 3......has a hyp of the square root of 13......which starts out..3.60.....full circle...


0 + 1 = 1
0 * 1 = 0

1 + 2 = 3
1 * 2 = 2

2 + 3 = 5
2 * 3 = 6

3 + 4 = 7
3 * 4 = 12

It is the 4th pair.................like 24.....like 11 + 13 = 24.....like 72/3 = 24...............like 2/4 = 1/2.......3 * 4 = 12.......12 is like 1/2, the c line.................2 + 2 = 4......2 * 2 = 4.....balance and a leap at 4..........for the 4th pair.............a line in the 4th dimension..................

Girl power!!  I hope you are well Adri.......................compare the sums and products..........

2, 3, 5, 7,
2, 4, 6, 8

The 1st 4 primes.......and the 1st 4 even numbers........like 14i..........and every even negative integer.............add the two lists.....straight down.......4, 7, 11, 15.................4 and 7......the 1st 10 numbers of e sum to 47..............47 is the last prime under 50......50 is half way from 0 to 100.......0 - 100...........adding them one by one...sum to 5050.....50 + 50 = 100.......fractal patterns...





a quantum leap at 4.....for successive pairs.....and one that resembles pi..3.14........

0 + 1 = 1
0 * 1 = 0

1 + 2 = 3
1 * 2 = 2

2 + 3 = 5
2 * 3 = 6

3 + 4 = 7
3 * 4 = 12

It is the 4th pair.................like 24.....like 11 + 13 = 24.....like 72/3 = 24...............like 2/4 = 1/2.......3 * 4 = 12.......12 is like 1/2, the c line.................2 + 2 = 4......2 * 2 = 4.....balance and a leap at 4..........for the 4th pair.............a line in the 4th dimension..................

Emmy Noether | German mathematician | Britannica.com

https://www.britannica.com/biography/Emmy-Noether

  

Emmy Noether, in full Amalie Emmy Noether, (born March 23, 1882, Erlangen, Germany—died April 14, 1935, Bryn Mawr, Pennsylvania, U.S.), German ...

Missing: sy ‎| ‎Must include: ‎sy

Symmetry is one of the major keys......fractal patterns..........4d.....the tesseract.....a square in a square.....like Russian dolls...............one inside the other.......2 3 dimensional objects........4d.........a quantum leap at 4.....for successive pairs.....and one that resembles pi..3.14........

0 + 1 = 1
0 * 1 = 0

1 + 2 = 3
1 * 2 = 2

2 + 3 = 5
2 * 3 = 6

3 + 4 = 7
3 * 4 = 12

It is the 4th pair.................like 24.....like 11 + 13 = 24.....like 72/3 = 24...............like 2/4 = 1/2.......3 * 4 = 12.......12 is like 1/2, the c line.................2 + 2 = 4......2 * 2 = 4.....balance and a leap at 4..........for the 4th pair.............a line in the 4th dimension..................

Emmy Noether | German mathematician | Britannica.com

https://www.britannica.com/biography/Emmy-Noether

 

Emmy Noether, in full Amalie Emmy Noether, (born March 23, 1882, Erlangen, Germany—died April 14, 1

So many 13's........the 1st 3 numerators of the simplified fractions......are 113........41, 43, and 47...sum top 131...............43 + 47 = 90...............like a right angle.........3 fours..........41, 43, and 47.......3 primes..................using just the double digits of each prime.....is 3 fours.....imp. b/c 3 + 4 = 7....3 * 4 = 12...................7 + 12 = 19..............1/9 + 1/10...a jump..........3 and 4 yield a "quantum leap".......for successive pairs............when u compare their products to their sums................


1/8, 2/8, 3/8, 4/8, 5/8, 6/8, 7/8, 8/8
1/8, 1/4, 3/8, 1/2, 5/8, 3/4, 7/8, 1/1....(1).............every other term simplifies.........all the primes do not...........................

The critical line at 1/2.....1/8th and 2/8th are the 1st two fractions...............just like the c line.....and 1828 in e..............3 - 10...........3 + 10 = 13............14.13i........the square root of 13 starts.....3.60555.........like full circle.....18281828 are the 3rd - 10th numbers in e........13 is the closest prime to the 1st zero and in its dec expansion........................

Fractal patterns.....chaos theory........10/8 is like 18.............and 5/4......which is the 3rd term of Euler's product with a s of 1...........and 1828459045 in e..............459045 is the 11 - 16th number in e.........and another fractal e....11 + 16 = 27.....also imp.......459045....is the 1st pattern of numbers greater than the 10th number in e....10 is the base.............a fractal pattern in itself..........7/4 is like 47.......the 1st 10 numbers of e sum to 47...........4 + 7 = 11.............11/10 is the 5th term of Euler's product..............................41, 43, 47....sum to 131...........and are the 1st 3 primes in a 0 to 0 ten digit sequence.............40 - 50..........45 again....like a 45/45 degree right triangle.................9 and 15......the two different ones...both divisible by 3.......the 2nd prime......9/3 = 3.........15/3 = 5............5/3 = 1.666......like the golden ratio.......................


9/8, 10/8, 11/8, 12/8, 13/8, 14/8, 15/8, 16/8
9/8, 5/4, 11/8, 3/2, 13/8, 7/4, 15/8, 2.....................

A person can do a lot if they try........put forth effort.......symmetry is very important..

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Noether's (first) theorem states that every differentiable symmetry of the action of a physical system has a corresponding conservation law. The theorem was proven by mathematician Emmy Noether in 1915 and published in 1918, although a special case was proven by E. Cosserat & F. Cosserat in 1909.

Fractions greater than 1...............half simplify, half do not.........1/9 + 1/10.....two 19s.....1828 1828...summed 1 by 1......yield two 19s.........as does the jump in the h.s.........from single digit denominators to double digit denominators....................8 up, 8 down..16 over all..........just like 1.618.....the golden ratio...............................5, 11, ,3, 13, 7, 15 .........and a whole number....2...........7 then 1...............2.71........e..........67, 71......the 1st prime pair to match one primes single digit to the next primes double digit.....the imp. part......connection.............15.........teh 1st 5 primes...connect single digits to double digits......and sum to 28....which is the 2nd perfect number.......and in 2 pi.........6.28..........which, when taken together...like that is the 1st 2 perfect numbers......6 and 28................9 and 15....................the 1st hill north of 1, 0 is at like 9.986i they tell me..............9 is imp. b/c its products add back up to 9......9 * 2 = 18...........9 * 3 = 27.......1 + 8 = 9......2 + 7 = 9......and are like some of the most imp. concepts in math.........


9/8, 10/8, 11/8, 12/8, 13/8, 14/8, 15/8, 16/8
9/8, 5/4, 11/8, 3/2, 13/8, 7/4, 15/8, 2.....................

The Music of the Primes said that B Riemann had found nature's winning lottery ticket......



9/8, 10/8, 11/8, 12/8, 13/8, 14/8, 15/8, 16/8
9/8, 5/4, 11/8, 3/2, 13/8, 7/4, 15/8, 2.....................



It is imp. to understand why that matches the other stuff.....patterns...........9 and 15......sum to 24........11 + 13 = 24.................72/3 = 24........2/4 = 1/2..................but 72/4 = 18.....1/8 is asymmetrical....compared to the 1st two interest rates...2 and 3...which are the 1st 2 primes.......it takes 36 years for money to double at a 2 % interest rate and 24 years for a 3% interest rate......36, and 24....both equal 1/2.........if you divide the double digit by the single digit.......2/4 = 1/2 3/6 = 1/2...........but 18 doesn't...........

68
95 
99


The 1st 3 standard deviations................6 +  8 = 14...........9 + 5 = 14.......99 is different.....9 + 9 = 18.....pi is everywhere.....9 * 2 = 18...............9 * 3 = 27.......an imaginary e.....9 * 4 = 36......full circle......

After 9/8..............also 9 + 8 = 17.......the 1st 4 primes, all in single digits, sum to 17..........2, 3, 5, 7..sum to 17...................the connection between addition and multiplication..1/2 + 14i........14i could stand for 1st 4.................1/2.....the 1st two.....single digits, double digits, etc...

9/8, 10/8, 11/8, 12/8, 13/8, 14/8, 15/8, 16/8.............the last is just like the golden ratio......which starts 1.618........................the dividing line is the other 1.......................every other term simplifies........every other negative integer.........16/8 = 2...........2 pi....2 is the both the 1st prime and the 1st even number............and kinda the 1st number....b/c 0 and 1 are so imp........both as numbers and expressions of a sort....b/c every number is a scaled version of 1....or the distance from 0 on the number line.............

9/8, 10/8, 11/8, 12/8, 13/8, 14/8, 15/8, 16/8
9/8, 5/4, 11/8, 3/2, 13/8, 7/4, 15/8, 2.....................

Also.............extracting the primes.................5, 11, 3, 13, 7..............2...............5 and a 1.............like 25 + 26 = 51......mag to iron............change in a star..........................i put separately.......b/c it is the only one that is not from  fraction.......................only 9 and 15 are not primes.................of the 8 on the bottom of the unit circle.......between pi and 2 pi....or 1 pi and 2 pi....like the c line 1/2...........6 are primes, 2 are not..........26....iron.........two of them.....one hidden, one seen.............light and darkness..............................

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Harmonic series

Music

A harmonic series is the sequence of sounds—pure tones, represented by sinusoidal waves—in which the frequency of each sound is an integer multiple of the fundamental, the lowest frequency. Wikipedia