Assume a fraction k/m, with 0≤k≤m and look at its digits written out
- The fraction has a finite number of digits (less m) OR is a repeated sequence with at the most m-1 digits per group
- A repeated sequence will have at the most n-1 zeroes next to each other, if the number is below 10ⁿ
- Interesting digit-structure of the sequence times m, with many 9’s (base minus 1) .
Continue reading “Numeric facts on fractions, that few are aware of.”
Obviously it is easy to calculate the diagonal of e.g. a sensor from the width and height with Pythagoras.
And a bit more tedious the other way round using the aspect ratio. [*]
But for common aspect ratios it is even simpler, 1+1/n fractions within less than 0.4%
Continue reading “Diagonal to width, simple fractions. Different aspect ratios”
A small rethought guide on calculating the day of week fairly easily
Continue reading “Calculate day of week”
Here Is a small guide in Disqus-formatting, that I have ‘published’ several times on the old GSMArena.com blog (with tiny variation).
UPDATE: Should in 2019 finally be more or less obsolete for wide enough windows!
Continue reading “Disqus-comments, formatting”
A nerdy idea:
A C# class that quicly can supply a lot of primes (here limited to about the largest prime about 50G – as arrays with over 2G entries are not currently supported without splitting the arrays)
A struct that supports basic arithmetic for large accurately represented numbers in Q, by factorization into primes.
A test program that tries to find solutions for a!b!=c! with 1<a<b<c
Continue reading “Working with numbers in Q with large nominator/denominator in C#”
For some reason, surprisingly few know this extremely simple formula, please share it.
I have actually seen in a carpet store an employee unrolling the carpet to measure the length!!
[The formula is simple to prove too… r=kφ, L=∫r dφ=∫kφ dφ=½k(φ2²-φ1²)=½k(φ2+φ1)×(φ2-φ1)=½(r2+r1) ×n2π=(r2+r1) × nπ , q.e.d.]