Maths equation circle and stamps

[HondoMan]

Odd title. Odd indeed.

I must be getting old and my maths were a very long time ago.  Seems there is an equation to solve this wee riddle.

Let's say I have a stamp that is 0,8mm long.  I need a circle in which the stamp will fit nicely without a gap between the first and last.  In order to figure out possible diameters, what would the equation be?

I can't for the bloody life of me recall. 

Anyone?

Cheers and have a nice start to the coming week,

~ Hondo

 

[YinTx]

Sketches help me understand what you are trying to solve... wasn't always the best at word problems without a sketch...

YinTx

[Northmount]

You need to start with an approximate diameter that you would like to end up with.  Calculate the circumference = 3.14 x diameter.  Divide the circumference by your stamp length 0.8 mm. (pretty small stamp)  Round the number up or down to a whole number.  Use that as you new circumference.  Divide by 3.14 to get your new diameter.

Tom

[LatigoAmigo]

I'm feelin' ya. I love math and math problems, but over the years the ways these kinds of questions are answered has slipped away, so these days I let software do the work.

Adobe Illustrator allows one to create a "pattern brush," so I made a circle with a diameter measuring 8 mm (0.8 is very tiny... can do that too), and made a circle with 24 of them. Let me know and I'll make you a template for any size and number that you'd like. It is very easy to do.

Twenty-four 8mm Circles.pdf

[Nuttish]

Do I understand correctly that you want to know the diameter of a circle around which you want to distribute a given whole number of smaller circles (enclosing your stamp)?

[Outfitr]

I usually just fit the stamp to whatever circle. I make sure to stop far enough in advance of the end to trial fit the stamp to see if I fudge it tight or a little loose to make it fit. Usually unnoticeable. 

[Rockoboy]

4 hours ago, Outfitr said:

fudge it tight or a little loose to make it fit. Usually unnoticeable

This is what I do, usually for the last 4 - 6 impressions, depending on how long, and what shape the run is.

[HondoMan]

On 4/8/2018 at 10:44 PM, YinTx said:

 

 

On 4/9/2018 at 0:54 AM, Northmount said:

 

 

On 4/9/2018 at 7:23 AM, LatigoAmigo said:

 

 

On 4/9/2018 at 9:26 PM, Nuttish said:

 

 

On 4/12/2018 at 5:26 AM, Outfitr said:

 

 

On 4/12/2018 at 10:20 AM, Rockoboy said:

 

Apologies for the late response.... the responses are truly appreciated.

As an example, I want the stamp below to fit properly around a circle.  I have yet to make the circle on leather.  I know the stamp has a length of 13mm, and I would like to know what diameter or circumference would be feasible so the stamp fits properly.  Imagine one makes the second to last stamp and there is an 9mm or 10mm gap.  That last stamp won't fit.  

What mathematical equation would assist?

Cheers!

 

 

 

 

[Northmount]

@HondoMan You need to propose an approximate outside diameter of the stamped circle.  We have no idea of your application, so obviously can't provide a solution.  Use my info from above with your preferred diameter and stamp length.

Tom

[Retswerb]

@HondoMan, let’s try as @Northmount suggested with the circle from your image above.

I’m going to guess those grid squares are 0.5 cm (5mm) apart. If so, your circle is app. 73 mm diameter. So, 73*3.14=229.22 for your circle’s circumference as drawn. 

Now divide circumference by stamp size: 229.22/13=17.63 - so you’re halfway between 17 stamp impressions and 18. Pick which you prefer - we’ll say 18 here - and multiply that number by stamp size to get a circumference that will work. 18*13=234 .

Now take that circumference and divide by 3.14 to get your diameter: 234/3.14=74.52 . To set your compass you need the radius, so divide by 2: 74.52/2=37.26mm.

Does that make sense?

[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.