Why do even the simplest calculators feature a square root key?

05082018, 06:07 AM
Post: #21




RE: Why do even the simplest calculators feature a square root key?
Hello,
I think it's the fact that square root is the natural extension of division 

05082018, 09:00 AM
(This post was last modified: 05082018 09:08 AM by Gamo.)
Post: #22




RE: Why do even the simplest calculators feature a square root key?
Today was thinking about the basic calculator on this thread about why it include the square root.
I found an article on how to calculate a "Display's Pixel Density" Definition: Pixel density is a metric telling us how many pixels there are in a fixed area of a display. It's a very important metric because it lets us know how closely packed the pixels on a display are. This is something that determines the quality, clarity, and readability of the image displayed. It is usually measured in a unit called pixels per inch (ppi). Very often, when we are confronted with evaluating the quality of a display and/or comparing two or more displays together, we don't have all the information available. Something that is often missing is the pixel density, which is actually a very important metric and can provide us with valuable information about the picture quality we could expect. But we almost always know the size (diagonal) of the screen given in inches and the resolution. Having this information we could easily calculate the pixel density ourselves. This is the formula: pixel density = √(Width^2 + Length^2) ÷ Screen Size Remark: screen size is the diagonal of the screen. Example using a basic calculator that included the square root Using Citizen FS50WHii model this one have [M+] feature. A computer display is 21.5 inch with 1920x1080 resolution Display size = 21.5 Inch Width = 1920 Length = 1080 Enter steps to calculate: 1920 x = M+ display 3,686,400 1080 x = M+ display 1,166,400 MRC display 4,852,800 √ display 2202.9071 ÷ 21.5 = 102.46079 Answer: Pixel Density = 102ppi (Close Approximation) So here is one of the good use of square root on a basic calculator. Gamo 

05092018, 06:16 AM
Post: #23




RE: Why do even the simplest calculators feature a square root key?
It's an interesting question, and I think there will be several answers
 the same thing happened with mechanical calculators: they evolved from add/sub to fourfunction to square root, and presumably for the same reason(s)  it's easy to implement square root, much easier than x^y or log or trig  an extra function makes for a more attractive product  it's a marketing arms race, and the electronic calculators might have been competing still with the mechanical ones  buyers will remember being taught to calculate square roots at school, as being the next algorithm you learn after long division  if buyers remember any formulae from school, the length of the hypotenuse and the solution of a quadratic are very likely to be in the list Of course, schooling has changed, and numeracy has changed, so it's harder to see now what would have been understood, what the competition would be, and what would have seemed attractive. It would be good to have a killer app for square root  it would be good to know why it was taught in schools, but it might not have been because it was useful. First mechanical calculator to offer square root, the Friden SRW in 1952: http://www.hpmuseum.org/srw.htm "The Friden SRW By the 1950's, four function motor driven mechanical calculators had become common on the desks of engineers and scientists. In 1952 Friden shook up the market with the SRW, with the amazing ability to extract a square root at the touch of a single key." http://www.hpmuseum.org/root.htm "How The Friden Extracted Square Roots  It's Basically What You Learned In School There are many ways to calculate a square root, and I'd be rather surprised if these early fivebangers used Newton's method. Square root is only about as expensive as division, and it wouldn't be normal to use lots of divisions to do the job. Here are some ways: http://user.mendelu.cz/marik/mechmat/sqrt/ 

05092018, 06:43 PM
(This post was last modified: 05092018 07:05 PM by dmmaster.)
Post: #24




RE: Why do even the simplest calculators feature a square root key?
(05092018 06:16 AM)EdS2 Wrote: It's an interesting question, and I think there will be several answers Modern Times, maths have changed a lot. 

05102018, 05:33 PM
(This post was last modified: 05102018 05:33 PM by pier4r.)
Post: #25




RE: Why do even the simplest calculators feature a square root key?
(05092018 06:43 PM)dmmaster Wrote: Modern Times, maths have changed a lot. Could you elaborate more on this? Maybe with 23 proper examples or analogies? I mean, 2+2 is still 4 in 1950 and in 2018 as far as I know. Wikis are great, Contribute :) 

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