Diagonal to width, simple fractions. Different aspect ratios

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%

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Disqus-comments, formatting

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!

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Working with numbers in Q with large nominator/denominator in C#

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

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Length of round (carpet) roll


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(φ21)×(φ21)=½(r2+r1) ×n2π=(r2+r1) × nπ , q.e.d.]