John Rostron

I have been looking at using svg to solve your problem. As a proof of concept, in Designer, I first created a simple background circle, with a single tick mark, then exported this to svg. I then grouped the tick mark and applied a couple of svg rotations and then opened this svg back into Designer.
This is the original with one tick:

and with two extra ticks added by editing the svg file.

The original svg had the following line for the tick:
<path d="M1181.1,590.551L1181.88,834.13" style="fill:none;stroke:black;stroke-width:2.22px;"/>
I grouped this, gave it an id of "line1" and then added a couple of transformed versions:
    <g id="line1">
    <path d="M1181.1,590.551L1181.88,834.13" style="fill:none;stroke:black;stroke-width:2.22px;"/>
    </g>
<use xlink:href="#line1" transform="rotate(10, 1173.02, 1173.02)" />
<use xlink:href="#line1" transform="rotate(45, 1173.02, 1173.02)" />

Note that the svg export converted my original units of mm to px. The 1173.02, 1173.02 is the centre of rotation in px.
I then looked at your formula for positioning the tick marks:
I then tried using the following  formula in  Excel:
=(LOG(SIN(E5*PI()/180)*10)*360)
the PI()/180 is because I assumed that the 0.1 ... 90 was in degrees. Applying this to the value 0.1 gives -632.924. Is this degrees? Subsequent values give -1.06718 for 5.7 and 87.82099 for 10. I would guess that the desired output from this should be degrees around a circle in the range: 0...360. Given a formula that created this range, it would be straightforward to use a combination of Excel and svg to create a svg file that created the desired tick marks.
Here is the svg file exported from my original Designer page and edited as above:
Ticks.svg
If you could check the formulas that you need to use, I could have another go and see if I can produce the goods.
My guess is that if you are trying to produce a circular slide rule, then it is just a matter of converting the degrees to a log scale, then scaling to fit around the circle.
John
 

That's the idea, but the background needs to stay blurred.  In the event, I've done some experimenting and it looks like AP selects a focussed area where one exists but doesn't touch the rest - exactly what I need!

Writing and illustrating a picture book. Using AD iPad for all the illustrations. Can you guess where it takes place :-)

Red Eyed Tree Frogs are native to Mexico, Central America and go all the way down to Colombia (perhaps on holiday). Its scientific name is A. callidryas, which comes from Greek words kalos (beautiful) and dryas (a tree or wood nymph).
I was chatting with someone about drawing and she liked to do Victorian style flora and fauna illustrations (I think there’s a proper name for it but I forget). I said that I usually try for realistic when I mess around for fun and she wanted to see something. One her favourite things are frogs, she has lots of ornaments etc in her house. So I did this, I think it might be the first living thing that I’ve done properly although I'll probably do a bit more to it sometime.
Just the pen tool, no textures.

 

You can copy and paste a 14 decimal place constant just as easily as a 2 decimal place one.
John

Yes, in the upper corner under "Develop" it should show 100% (see attachment).
What settings did you use for the detail refinement ?
 

I was speculating on how Equations could be used to create a ripple-like effect in a reflection. I used an image of a Mill on the River Avon at Tewkesbury. I flipped the image vertically and then applied Filter > Distort > Equations as follows.
The main effect is to vary the position of each pixel on the y-axis in a sinusoidal fashion, so I began with:
y=y+100*sin(2*360*y/h)
The 100 is just a scaling factor for now. This had the right effect but was the same right across the image, so I added a cosine function which would vary the magnitude across the x-axis:
y=y+100*cos(10*x/w)*sin(2*360*y/h)
Again the 10 here is a scaling factor. The result was:
 
I should be able to tweak this into a macro where the user could vary the amplitude of the ripple, and the amplitude of the horizontal variation.
A further tweak could be to add a perspective effect so that the ripples nearer the observer look larger than those further away.
What do possible users think. Would this be a useful macro or are there easier ways to get the same effect?
John

I think that a mnemonic that relies on a variant spelling is of less than optimal utility.
John

I’ve just re-read this and spotted a slight problem: “Archimedes” has 10 letters!
Edit: Found it!
https://www.mnemonic-device.com/arithmetic/pi/may-i-have-a-large-container-of-coffee/

I told you that it was what I recalled. I did not say my recollection was accurate. I met this mnemonic at school, probably over sixty years ago!
John

That rings a vague bell, John. The mnemonic I know is
One nice touch is that it even includes a comma for the decimal separator after ‘Sir’ (3). I find it almost as easy to remember a string of twenty digits, which has the advantage that you don’t need to do any counting, but it’s good to have a mnemonic to fall back on if you get lost somewhere along the way!

Ended up with this version.
 

Hi E9B6
Publisher doesn't currently naively support formulas within a table, akin to an Excel spreadsheet, my apologies.
You can add mathematical symbols through Text>Insert>Mathematics however these are simply glyphs and not active formulas.
I recommend checking out the following threads regarding equation support!
 

Yes exactly.  Let's keep it where I posted originally.
When I see people reply elsewhere or ask questions -- I just reply wherever I see them post.

(I already replied to the post in the other thread, FYI)

You can copy and paste a 14 decimal place constant just as easily as a 2 decimal place one.
John

I have the driver software installed which Affinity Photo (and photoshop Elements) use to scan directly into the software.
I also have Epson's own scan utility which works fine and I can load the output from that into Affinity or any other image editing software. Yes, that is perfectly possibly. My point was that there seems to be a bug in Affinity which prevents it acquiring the image correctly. Such a bug should be addressed. I raised this on the Forum as there seems to be no other way of reporting bugs, or potential bugs.
 
Jack

It scans into Affinity Photo but the result is useable. See my post further up with attachment Archive.sit. It has 2 images, one from Affinity and the other from Photoshop Elements, both using the same driver. The result from Affinity doesn't have even a remote resemblance to what it should look like.
Yes when I say Photos, I meant Affinity Photo. I don't use Apple Photos.
 
Jack

thats weird.   maybe the new build isn't fully cooked with vibrance?  not sure.

Sunday’s practice. Shapes and curves , self made vector brushes . 

If you search for "tiles using affine" (including the quotes), you should find some helpful threads.
John

Thanks guys for the responses.

An intriguing pair of designs. It has elements of many scientific displays I have seen. This time I do not have to try and interpret them because there is nothing to interpret. Just admire the visual appearance. 
Well done!
John

Conceded!
John

That even works with multiple layers. Just select them all, Copy, and New from Clipboard.

If you just want to change the width for one photo at a time, why do you need a macro? You can simply load the photo, go to the Transform panel, link the W and H controls to lock the aspect ratio, and then type in whatever value you want for the width.