High School Arc formula without the use of radius and angle

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SUMMARY

The discussion centers on a user who has developed a formula for calculating the arc length of a circle without using the radius or angle. The proposed formula is expressed in terms of the distance between the starting and ending points of the arc (denoted as x) and the breadth of the arc. Another participant suggests a formula involving the chord length (x) and the distance from the midpoint to the center of the circle (p), specifically $$2\sqrt{(x/2)^2+p^2}\tan^{-1}(x/2p)$$. The conversation concludes with concerns about publishing the formula and the potential for copyright issues.

PREREQUISITES
  • Understanding of arc length calculations
  • Familiarity with trigonometric functions, particularly tangent and inverse tangent
  • Knowledge of geometric concepts such as chords and circle properties
  • Basic principles of publishing mathematical formulas
NEXT STEPS
  • Research methods for publishing mathematical formulas online
  • Learn about the implications of copyright in mathematical expressions
  • Explore advanced trigonometric identities and their applications in geometry
  • Investigate alternative methods for calculating arc lengths without traditional parameters
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Mathematicians, educators, and students interested in geometric formulas, as well as individuals looking to publish original mathematical work.

Danishk Barwa
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I had created a formula on arc of a circle...How can I publish it ..So that people see it and decide is it important or not.
 
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There are exactly three possibilities: either it is wrong, well known, or useless.
 
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Danishk Barwa said:
I had created a formula on arc of a circle...
Out of idle curiosity, what is your formula?
 
I assume that you are talking about a formula for the arc length that does not use the radius or angle. My first question is how one can even specify an arc without the radius and the angle (in one form or another)?
 
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FactChecker said:
I assume that you are talking about a formula for the arc length that does not use the radius or angle. My first question is how one can even specify an arc without the radius and the angle (in one form or another)?
My formula is in terms of distance between starting and ending point of arc(x). And breadth of arc (distance between mid point x and mid point
 
Mark44 said:
Out of idle curiosity, what is your formula?
Please suggest me how to publish it
 
What is your concern about showing it here? Do you think there is some copyright privilege that you will give up and that someone will steal it?
 
Mark44 said:
Out of idle curiosity, what is your formula?
Danishk Barwa said:
My formula is in terms of distance between starting and ending point of arc(x). And breadth of arc (distance between mid point x and mid point
So ##x## is the length of the chord across the arc? Calling the distance from its midpoint to the centre of the circle ##p##, I make the arc length $$2\sqrt{(x/2)^2+p^2}\tan^{-1}(x/2p)$$
 
FactChecker said:
What is your concern about showing it here? Do you think there is some copyright privilege that you will give up and that someone will steal it?
Yes
 
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Ibix said:
So ##x## is the length of the chord across the arc? Calling the distance from its midpoint to the centre of the circle ##p##, I make the arc length $$2\sqrt{(x/2)^2+p^2}\tan^{-1}(x/2p)$$
No..That's not correct ...You please tell me how and where to publish it
 
  • #11
Danishk Barwa said:
You please tell me how and where to publish it
Since you do not wish to divulge the formula you have created, we have no way of discerning whether it is useful or original.

Thread closed.
 

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