Editing Mathematical coincidence (section)

==== Concerning base 2 ====
* The coincidence <math>2^{10} = 1024 \approx 1000 = 10^3</math>, correct to 2.4%, relates to the rational approximation <math>\textstyle\frac{\log10}{\log2} \approx 3.3219 \approx \frac{10}{3}</math>, or <math> 2 \approx 10^{3/10}</math> to within 0.3%.  This relationship is used in engineering, for example to approximate a factor of two in [[Electric power|power]] as 3&nbsp;[[decibel|dB]] (actual is 3.0103&nbsp;dB – see [[Half-power point]]), or to relate a [[kibibyte]] to a [[kilobyte]]; see [[binary prefix]].<ref>
{{cite book
 | title = Matlab und Simulink
 | author = Ottmar Beucher
 | publisher = Pearson Education
 | year = 2008
 | isbn = 978-3-8273-7340-3
 | page = 195
 | url = https://books.google.com/books?id=VgLCb7B3OtYC&q=3.0103+1024+1000&pg=PA195
}}</ref><ref>
{{cite book
 | title = Digital Filters in Hardware: A Practical Guide for Firmware Engineers
 | author = K. Ayob
 | publisher = Trafford Publishing
 | year = 2008
 | isbn = 978-1-4251-4246-9
 | page = 278
 | url = https://books.google.com/books?id=6nmnbIxpY3MC&q=3.0103-db&pg=PA278
}}</ref> The same numerical coincidence is responsible for the near equality between one third of an octave and one tenth of a decade.<ref>Ainslie, M. A., Halvorsen, M. B., & Robinson, S. P. (2021). A terminology standard for underwater acoustics and the benefits of international standardization. IEEE Journal of Oceanic Engineering, 47(1), 179-200.</ref>
* The same coincidence can also be expressed as <math>128 = 2^7 \approx 5^3 = 125</math> (eliminating common factor of <math>2^3</math>, so also correct to 2.4%), which corresponds to the rational approximation <math>\textstyle\frac{\log5}{\log2} \approx 2.3219 \approx \frac{7}{3}</math>, or <math> 2 \approx 5^{3/7}</math> (also to within 0.4%). This is invoked in [[Preferred number|preferred numbers]] in engineering, such as [[shutter speed]] settings on cameras, as approximations to powers of two (128, 256, 512) in the sequence of speeds 125, 250, 500, etc.,<ref name=schroeder/> and in the original ''[[Who Wants to Be a Millionaire?]]'' game show in the question values ...£16,000, £32,000, £64,000, '''£125,000''', £250,000,...