What are the latest research developments on Heron's Formula?

In summary, the conversation revolved around researching and proving Heron's Formula, with the main question being what new information or application could be discovered about a well-known and tested formula. The conversation also touched on the legality of proving something that has already been proven, as well as the challenge of expanding a short proof into an 8-page paper. The topic of discussion then shifted to a comparison of Derivatives and Averages and which one would be more sensible in numbers, with the added challenge of explaining complex math concepts to a non-mathematical audience. Overall, the conversation highlighted the complexities and nuances of conducting and presenting mathematical research.
  • #1
PrudensOptimus
641
0
Research on Heron's Formula??/

Today I saw a guy entitling his Research paper with "Heron's Formula." I asked him ... what can you do with a equation that has been tested for hundreds of years... he said nothing.

I wonder what can you research about that. And any good Math researches? And can you even research pre-existing stuff?
 
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  • #2
One, what "level" research was this? (High school or college term paper, graduate work, published research?)

Two, what was the point of the paper? (New application, history, etc.)

Certainly, if you have something new to say about anything that other want to hear, you can write it. Of course, the editors and referees of the journal where it is published (or teacher or professor to whom the paper is submitted) will decide whether it really is new and if anyone really wants to hear it!

If you are talking about "research" that is "published" on a web-site, well, that could be anything.
 
  • #3
It's for a sophmore Science Fair thing... He said he will proove the Heron's Formula in the research paper... I saw the proof many times, starting from 0.5Sin[A] * a, and replacing Sin[A] with sqrt(1 - Cos 2A/2)... and then a lot of factoring and math comes to the well known form of sqrt(s(s-a)(s-b)(s-c)), s = a+b+c/2

But is it even ... legal to proove a law tested billions of times? That's ... bs lol.
 
  • #4
As far as I know there are no laws about proofs!

Yes, it is perfectly "legal" to prove something that has been proven before- teachers do it all the time. It is even legal to exactly copy someone else's proof as long as:
1) You give credit to the person or
2) It was done long enough ago that it is in the public domain.

As to how much credit the judges of the science fair will give it, I'll leave that up to the judges.
 
  • #5
Out of curiousity,... what would the intro, abstract, experiment, ... would be when you are doing a proof? ... for the most the proof is 20 lines... how would you make that long enough to fit 8 pages?(min req. for page is 8 pages long).

I am doing a comparison of Derivatives to Averages, which one would be more sensible in numbers., And ... because my teacher who would be reviewing it is a chemistry teacher,... knows nothing about fancy math, not even simple math..., I really don't want to irritate her with math... So I used ... 300 words just to describe the limit defination of derivative... that's soo bs... anyways, how would you do math "discussing" papers (not really research to me, because is not really a breakthrough., just talking about which one might be more sensible)
 

1. What is Heron's Formula and how is it used in research?

Heron's Formula is a mathematical formula used to calculate the area of a triangle based on the lengths of its sides. In research, it is often used to find the area of irregular or non-standard shapes, which may be encountered in various fields such as engineering, physics, and geography.

2. Who discovered Heron's Formula?

Heron's Formula was discovered by a Greek mathematician, Heron of Alexandria, in the 1st century AD. It was originally known as the Hero's Formula and was later renamed to honor its discoverer.

3. How is Heron's Formula derived?

Heron's Formula is derived from the Pythagorean Theorem and the Law of Cosines. By using these two principles, it is possible to derive a formula that can be used to calculate the area of any triangle, regardless of its shape or size.

4. What are the advantages of using Heron's Formula over other methods?

Heron's Formula is advantageous because it can be used to find the area of any triangle without needing to know the height or base length. It also works for all types of triangles, including acute, right, and obtuse triangles. This makes it a versatile and efficient tool for researchers.

5. Are there any limitations to using Heron's Formula?

While Heron's Formula is a useful tool, it does have some limitations. It requires the lengths of all three sides of the triangle, which may not always be known. It also involves more complex calculations compared to other methods, which may be a disadvantage for some researchers.

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