Arithmetica & Musica 16th Century Roman Greek Goddess
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After looking for a long time, I finally found this #Sliderule, which belonged to my late father. Some of you will know that these #devices were used, before the advent of digital #Calculators, to perform #arithmetic operations such as #multiplication and #division to about three significant figures, by #scientists and #engineers.
#Mathematics #Computation (1/2)
@RobertoArchimboldi
(-m)(-n)+(-mn)=(-m)(-n+n)
(-m)(-n)+(-mn)=(-m)(0)
(-m)(-n)+(-mn)=0
(-m)(-n)=mn
#maths #HopeThisHelps #arithmetic #math
A short story about my decomposition into weight × level + jump. It's a new fundamental theorem of arithmetic and academia is 11 years late.
#decompwlj 
It's a decomposition of positive integers. The weight is the smallest such that in the Euclidean division of a number by its weight, the remainder is the jump (first difference, gap). The quotient will be the level. So to decompose a(n), we need a(n+1) with a(n+1)>a(n) (strictly increasing sequence), the decomposition is possible if a(n+1)<3/2×a(n) and we have the unique decomposition a(n) = weight × level + jump.
We see the fundamental theorem of arithmetic and the sieve of Eratosthenes in the decomposition into weight × level + jump of natural numbers. For natural numbers, the weight is the smallest prime factor of (n-1) and the level is the largest proper divisor of (n-1). Natural numbers classified by level are the (primes + 1) and natural numbers classified by weight are the (composites +1).
For prime numbers, this decomposition led to a new classification of primes. Primes classified by weight follow Legendre conjecture and i conjecture that primes classified by level rarefy. I think this conjecture is very important for the distribution of primes.
It's easy to see and prove that lesser of twin primes (>3) have a weight of 3. So the twin primes conjecture can be rewritten: there are infinitely many primes that have a weight of 3.
I am not mathematician so i decompose sequences to promote my vision of numbers. By doing these decompositions, i apply a kind of sieve on each sequences.
https://oeis.org/wiki/Decomposition_into_weight_*_level_%2B_jump
Arithmetic has a biological origin. Arithmetic is not a human invention but a natural phenomenon that emerges from how our brains perceive and process sensory information. Our brains use symbols, such as numbers, to represent and manipulate the patterns and structures of reality. Arithmetic could be a universal language that connects us with other intelligent beings.
Remember awhile back, there were videos to explain the difference between a million dollars vs a billion dollars. 
Using Rice:
https://youtu.be/qSOVBiEotaw
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