Square Root and Radical Sign: geometry found in the sign. A proof here.

[notorab]

The radical or square root sign contains geometry in itself the computes the square root.  I prove this at this link.  Asking this community for advice because I think this falls under typography.

 

https://math.stackexchange.com/questions/4978928/square-root-radical-symbol-is-geometry-of-the-symbol-specifying-mathematics-u

 

https://math.stackexchange.com/questions/4978928/square-root-radical-symbol-is-geometry-of-the-symbol-specifying-mathematics-u

[Ralf Herrmann]

Much like the people on StackExchange, I am not convinced. 

[Riccardo Sartori]

In most cases, rationalisation is a post facto operation. See, for example, the works of Albrecht Dürer and Luca Pacioli on the Roman capitals.

Also always be ware of spurious correlations.

[notorab]

Did you look at the graphic with e, 1 and sqrt(e)?  Measure 1 length on the symbol, then measure e.  Divide e length on symbol by 1 measurement call this A.  Divide sqrt(e) length on symbol by 1 measurement on symbol, call this B.  A will be 2.7... .  Now on calculator get sqrt(2.7), it will equal B.  Do you think the symbol was randomly chosen?  Also check out the other post linked in beginning for sqrt of 2.  The lines match right up to the geometric explation with square and circle.

 

[notorab]

I want to comment the argument by on math SE was about the symbol being random lines scribbled and no sense could be made.  It is not on the computation or measurement, because I establish a unit 1 shown on the symbol.  I argue to SE contributors, the symbol is used everywhere for square root operations, so we know it involves taking the square root.  Therefore, the probability the author of symbol included operation of square root in geometry of the symbol itself is high.  Why would it be random scribbles.  Also, check out that letter 'r' and 'R' was historically used for square root.  The old letter in Roman Cursive looks like the square root symbol I show it.  Also check on the link to geometry of sqrt(2).   The modern symbol fits right over the circle and square with lengths matching.  Its rather surprising to see it.

[notorab]

11 minutes ago, Riccardo Sartori said:

In most cases, rationalisation is a post facto operation. See, for example, the works of Albrecht Dürer and Luca Pacioli on the Roman capitals.

Also always be ware of spurious correlations.

 

[notorab]

Helpful!! I see 1525 Albrecht Dürer here:

https://archive.org/details/vnderweysungderm00drer/page/n7/mode/2up

His Roman capitals start at page 115 for the PDF.

Already looking at B, I see the slope of y=(1/e)x+b in his geometry. I posted this on SE site for 'e' itself.  Interesting history says Euler had correspondence with Leibniz originally using letter B to represent the exponential function e^1=2.7... He starts lowercase construction Blackletter on page 139 looks and it's made with unit squares. Page 141 has uppercase Blackletter, but no explanation on creating the letters. On page 142, he shows a bunch of NETs, but without knowing German here I have no idea if they are related to Blackletter construction.

 

I can't find anything from Luca Pacioli, do you have pointers here?

 

Again, helpful on construction of letters of Serif'd Latin script and lowercase Blackletter for Durer's time. It's missing uppercase Blackletter and it would be helpful if there were better exemplars of it.

 

Also, just note:

I'm looking for geometric semantics on the intended operation/function of the letter if they exist.  For instance I show in posts on SE, letter 'e' from 700AD Old English has mathmatical constants and math spirals using constant e in letter.  I show square root / radical even a Roman Cursive 'r' that resembles the radical sign and square root operation taken with length (using a common unit), then square root of 2 with geometry.

 

Agreed on spurious, conclusive theory will require statistical analysis of many exemplars.  Also, my theory is letters in handwritten script may change geometry depending on the meaning conveyed in them.  For instance, I show on SE letter 'e' changes geometry, but constants remain the same.  The author could change it in cursive as a way of communicating.  Look at Greek Byzantine script, its very cursive and letter geometry changes throughout the document.

 

Again, thanks for your guidance!

 

[notorab]

You suggest Durer's document which has Blackletter script in it.  Actually his whole manuscript is in Blackletter.  Curious if anyone here has better exemplars of uppercase versions and perhaps a document showing geometry how the letters are constructed.  

[notorab]

For your spurious correlation link it shows graph that is correlated spuriously.  I would mention the two variables in the graph, do not share a common unit like 1.  One is a scalar multiple of the other, which is how they are spuriously correlated as equivalent.