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

[Pekis]

Hello,

I think it's the fact that square root is the natural extension of division

[Gamo]

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 FS-50WHii 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

[EdS2]

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 four-function 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 five-bangers 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/

[dmmaster]

(05-09-2018 06:16 AM)EdS2 Wrote:  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 four-function 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 five-bangers 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/

Modern Times, maths have changed a lot.

[pier4r]

(05-09-2018 06:43 PM)dmmaster Wrote:  Modern Times, maths have changed a lot.

Could you elaborate more on this? Maybe with 2-3 proper examples or analogies?

I mean, 2+2 is still 4 in 1950 and in 2018 as far as I know.