Editing Fibonacci sequence (section)

===Other===
* In [[optics]], when a beam of light shines at an angle through two stacked transparent plates of different materials of different [[refractive index]]es, it may reflect off three surfaces: the top, middle, and bottom surfaces of the two plates. The number of different beam paths that have {{mvar|k}} reflections, for {{math|''k'' > 1}}, is the {{mvar|k}}-th Fibonacci number. (However, when {{math|1=''k'' = 1}}, there are three reflection paths, not two, one for each of the three surfaces.){{sfn|Livio|2003|pp=98–99}}
* [[Fibonacci retracement]] levels are widely used in [[technical analysis]] for financial market trading.
* Since the [[conversion of units|conversion]] factor 1.609344 for miles to kilometers is close to the golden ratio, the decomposition of distance in miles into a sum of Fibonacci numbers becomes nearly the kilometer sum when the Fibonacci numbers are replaced by their successors. This method amounts to a [[radix]] 2 number [[processor register|register]] in [[golden ratio base]] {{mvar|φ}} being shifted. To convert from kilometers to miles, shift the register down the Fibonacci sequence instead.<ref>{{Citation | url = https://www.encyclopediaofmath.org/index.php/Zeckendorf_representation | contribution = Zeckendorf representation | title = Encyclopedia of Math}}</ref>
* The measured values of voltages and currents in the infinite resistor chain circuit (also called the [[resistor ladder]] or infinite series-parallel circuit) follow the Fibonacci sequence. The intermediate results of adding the alternating series and parallel resistances yields fractions composed of consecutive Fibonacci numbers. The equivalent resistance of the entire circuit equals the golden ratio.<ref>{{citation
 | last1 = Patranabis | first1 = D.
 | last2 = Dana | first2 = S. K.
 | date = December 1985
 | doi = 10.1109/tim.1985.4315428
 | issue = 4
 | journal = [[IEEE Transactions on Instrumentation and Measurement]]
 | pages = 650–653
 | title = Single-shunt fault diagnosis through terminal attenuation measurement and using Fibonacci numbers
 | volume = IM-34| bibcode = 1985ITIM...34..650P
 | s2cid = 35413237
 }}</ref>
* Brasch et al. 2012 show how a generalized Fibonacci sequence also can be connected to the field of [[economics]].<ref name="Brasch et al. 2012">{{Citation| first1 =T. von | last1 = Brasch | first2 = J. | last2 = Byström | first3 = L.P. | last3 = Lystad| title= Optimal Control and the Fibonacci Sequence |journal = Journal of Optimization Theory and Applications |year=2012 |issue=3 |pages= 857–78 |doi = 10.1007/s10957-012-0061-2
|volume=154 | hdl = 11250/180781 | s2cid = 8550726 | url = https://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-24073 | hdl-access = free }}</ref>  In particular, it is shown how a generalized Fibonacci sequence enters the control function of finite-horizon dynamic optimisation problems with one state and one control variable. The procedure is illustrated in an example often referred to as the Brock–Mirman economic growth model.
* [[Mario Merz]] included the Fibonacci sequence in some of his artworks beginning in 1970.{{sfn|Livio|2003|p=176}}
* [[Joseph Schillinger]] (1895–1943) developed [[Schillinger System|a system of composition]] which uses Fibonacci intervals in some of its melodies; he viewed these as the musical counterpart to the elaborate harmony evident within nature.{{sfn|Livio|2003|p=193}} See also {{slink|Golden ratio|Music}}.