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Get formula to calculate text rotation angle (clock angle problem)?

Posted 4 months ago
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Hello. Let's say we have circle. We cut it to 4 'triangles' but longest hand is perfect arc. I want to write some letters on this arc but rotate it to be horizontal always. In other words, how to make clock face with horizontal numbers. It can be any hour, so can be 12-3-6-9, but can be 1-4-7-11 etc. Thanks for suggestions.

Posted 4 months ago

The description is not very clear. Do you mean something like this?

numbers = Range[12];
angles = Table[i*2*Pi/12, {i, 1, 12}];
numberAngles = AssociationThread[numbers, angles];
  Circle[{0, 0}, 10],
  Text[Style[#, 14, Blue, Bold], {9 Sin[numberAngles[#]], 9 Cos[numberAngles[#]]}] & /@ {1, 4, 6, 7, 11}}]

enter image description here

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