Maths equation circle and stamps

[Retswerb]

A couple of caveats to add: 

- Your stamp looks more like 12 than 13 to me, per your picture.

- You have to decide whether you’re putting the inside, outside, or middle of the impression on the circumference line, and adjust accordingly. If you stamp outside the line all the way around they will line up nicely, but the tops of your impressions won’t be touching - so some further adjustment / trial may be needed if you really want it to be perfect.

[Instinctive]

This might help. You will need to trial and error the calculations to get the size you want to have an even number of stamps.

N= Number of stamps for the circle

L= length of Stamp

D= Diameter of Circle

If you know the number of stamps you want:

D=(NxL)/3.14

Example:

N=20

L=13

D=(20x13)/3.14
 = 260/3.14

D=82.8 ~ 83 mm

If you have a diameter of circle in mind.

N=(Dx3.14)/L

Example:

D=100

L=13

N=(100x3.14)/13
 =314/13

N=24.15 stamps.

Adjust diameter to make even number of stamps. In this case a diameter of 99.5 mm = 24 stamps (that's likely being a bit too accurate :-)

Either way, measure twice, cut once and do a practice piece.

 

[HondoMan]

@Instinctive, I know neither the number of stamps nor a diameter. 

All me to explain it this way.  If I have a stamp with a length of 5mm or 10mm, I know that straight lines with a length divisible by 5 or 10 (20cm, 40cm, 100cm, etc.), will allow me to stamp along this line with no gaps at the beginning or end. 

With that said, mate, I have the same 10mm stamp and I want to use it around a circle.  I need a mathematical formulae to determine possible circumferences so there is no gap between stamps around the end of the circle.  If I wanted to put circles inside circles with a stamp along the edge or between circles, I would need to know several circumferences.  This is what I am on about.
 

[gigi]

Below is the formula for the length of a chord. Given the stamp length (=length of the cord) and the angle (depending on how many stamps you apply ).

You just need to extract the radius of your circle from the formula bellow: 

[Instinctive]

4 hours ago, HondoMan said:

@Instinctive, I know neither the number of stamps nor a diameter. 

All me to explain it this way.  If I have a stamp with a length of 5mm or 10mm, I know that straight lines with a length divisible by 5 or 10 (20cm, 40cm, 100cm, etc.), will allow me to stamp along this line with no gaps at the beginning or end. 

With that said, mate, I have the same 10mm stamp and I want to use it around a circle.  I need a mathematical formulae to determine possible circumferences so there is no gap between stamps around the end of the circle.  If I wanted to put circles inside circles with a stamp along the edge or between circles, I would need to know several circumferences.  This is what I am on about.
 

If you know the straight line length = X

Circle diameter D=X/3.14

[charon]

Basically everything has been said. Since I also went to a German school I throw in my $0.02. The circumference of a circle is U = 2 * pi * (radius of your circle). So, basically as Instinctive says, you have to choose your radius in a way that the circumference U divided by the length of your stamp is an even number. To me the stamp also looks like 12mm, so your U has to be a multiple of 12 (but at least lets say 6*12, since you want to go round). As Retswerb said, you have to choose whether you set your stamp outside, inside or on the circumference line of your circle. I assume you put it outside, which means the inside of the stamp aligns and the outside doesn't. To be perfect, You'd have to transform your circle to an n-edge (German: "n-Eck"), whith the length of n being the length of your stamp. If I were you I'd do the following: Since only one side of the stamp will align because you are going round with a straight stamp as already has been said, I'd take a divider, draw a circle on a piece of paper and draw 12mm tangents around it until you like the result.

You don't mention how big your circle is going to be. However, just from the maths I would start with a radius of 21mm, which gives a circle with a circumference of 132mm, which are exactly 11 stamps of 12mm length. Adjust from there..

[LatigoAmigo]

This table shows the radius of the circle based on the number of stamp imprints that will fit into that circle. Hope it helps.

# of Stamp Imprints	Radius in mm
8	15.28
9	17.19
10	19.10
11	21.01
12	22.92
13	24.83
14	26.74
15	28.65
16	30.56
17	32.47
18	34.38
19	36.29
20	38.20
21	40.11
22	42.02
23	43.93
24	45.84
25	47.75
26	49.66
27	51.57
28	53.48
29	55.39
30	57.30

[Nuttish]

13 hours ago, HondoMan said:

@Instinctive, I know neither the number of stamps nor a diameter. 

All me to explain it this way.  If I have a stamp with a length of 5mm or 10mm, I know that straight lines with a length divisible by 5 or 10 (20cm, 40cm, 100cm, etc.), will allow me to stamp along this line with no gaps at the beginning or end. 

With that said, mate, I have the same 10mm stamp and I want to use it around a circle.  I need a mathematical formulae to determine possible circumferences so there is no gap between stamps around the end of the circle.  If I wanted to put circles inside circles with a stamp along the edge or between circles, I would need to know several circumferences.  This is what I am on about.
 

That's exactly what the equation I gave does. You wish to know the circumference of the circle around which you wish to stamp. You already know the number of impressions and size of the stamp. Plug and chug.

[gigi]

Honestly, even if I know the circumference and number of impressions, chances are: I will not stamp perfectly. If the stamp is for example rectangular and  two corners of the the stamp are resting on the circle line: that way the alignment will be better, I think. 

I usually stamp until I get closer to the end of the circle, and then I estimate if the last impressions should be a bit more spaced.