@acer At the moment I am busy with another project, so it will be some time before I can try your suggestion. I confirm that am needing a search of 2D input.

On first impression, among the other replies received, I like yours best because it is all within Maple and because you have taken the trouble to originate it.

@gkokovidis Thank you for your suggestion. Now that I have received a number of suggestions, it may take some time for me to try this and I'll report back to you when I do

@rlopez Thank you for your suggestion. It may take some time for me to try this and I'll report back to you when I do.

@acer Thanks for the suggestion.

I'll try it, but to process more than one hundred worksheets this way is intimidating.
A similar approach could be to export each worksheet to Rich Text format, which should  be text searchable.

From your and Carl Love's replies it seems there may be no way to easily search a large number of worksheets.

@Carl Love Unless I've missed one of its capabilities Windows File Explorer will only find words in folder and file names and within text files but not in Maple worksheets.

@acer Thank you for showing me that the problem was one of the difference in precision of the numbers between the two BinarySearch commands. When I use numbers of the same precision the command produces the correct result.

The procedure works well for the few combinations of p,q I tried except the fsolve command produces an error for p,q = 2,3 (Coxeters loxodromic sequence of tangent circles).

A change of plottools:-circle to plottools:-disk displays neither circles nor disks.

@dharr In the next while I will work on understanding the logic of your answer and ask you to clarify anything that puzzles me.

You have given me much to enjoy and probably some new insights to geometry. Thank you!

@dharr I thank you for your reply, however Maple apparently cannot convert even the first few lines of the Mathematica code in the website to which you provided the link.

I am completely unfamiliar with this conversion so it is likely that I am doing it incorrectly using the command MmaToMaple.

Website https://en.wikipedia.org/wiki/Coxeter%27s_loxodromic_sequence_of_tangent_circles contains some specifications for the Coxeter version of the Doyle spiral but nothing describing the logarithmic spirals on which the tangent circles have their centrers.

@vv I will examine the answer in the link you have provided. Hopefully it will give me some insight into the Doyle spiral's math.

Here is a geodesic on a lumpy sphere.

Geodesic_on_a_lumpy_sphere.mw

I couldn't figure out how to display the geodesic path using standard plot commands.

@Rouben Rostamian  Thank you taking the time to explain Wikipedia's "in some sense". 

@Rouben Rostamian  Thanks for sending me this lovely picture, but shouldn't a geodesic be the shortest distance between the two points shown? If that is true then can your earlier statement about an infinity of geodesics between two points be true?

I probably won't be able to try to find geodesics on other surfaces until past this weekend.

@Rouben Rostamian  This is wonderfully simpler than your previous answer and more understandable at my level of math capability.

It is fascinating that a different geodesic is produced merely by stating the same end point in a different way!

I would try to choose this reply as a second best answer but I'm afraid that might screw up this website.

I will try this method for different surfaces, and if you do so please send me the results if they are interesting.

@Rouben Rostamian  Thanks for doing this lookup. I'll see what I can find (and understand).

Is this paper of any value?

https://www.pearson.com/content/dam/one-dot-com/one-dot-com/us/en/files/Jay%20Villanueva%20-%20geodesics9.pdf