Heron's Formula

[gogopoco]

Is there any point in analyzing Heron's Formula to get useful results? If not, could you please suggest other formulas, postulates, or theorems that would work? Thanks.

[deleted-2574]

Hi gogopoco,,

That's an interesting formula you bring up, one that I hadn't heard of despite majoring in mathematics many eons ago.

Heron's formula has a practical use: one can compute the area of a triangle while measuring only the lengths of the three sides. The wikipedia entry for Heron's formula:

http://en.wikipedia.org/wiki/Heron's_formula

has the formula and two proofs.

Two other sources of information are at:

http://mathworld.wolfram.com/HeronsFormula.html
http://www.mathopenref.com/heronsformula.html

The second reference above has an interactive Heron's formula calculator.

[gogopoco]

Thanks for the help. but I don't know if it's useful to anaylze different ways of proving Heron's Formula. Could you please help me?

[deleted-2574]

Hi gogopoco,

I agree, the proof of Heron's formula is not of practical value. What is of practical value is the formula itself. It's good to know that there is a proof of the formula (and the proof has stood the test of time). The proof allows you to apply the formula to calculate area with a certainty that the returned area value is correct.

It's not necessary to understand the proof or be able to reproduce it in a test. (And the proof is not at a grade 6-8 level.) Note: in the discussion above, "proof" refers to "proofs" (since there are two).

[deleted-71677]

Hi Gogopoco! Are you looking at Heron's formula for a science fair project, or for a class assignment, or for a test in school? Let us know what has been asked of you, and we will better be able to answer your question.

laura

[gogopoco]

It's for a science fair project.
One last question: If Heron's Formula is not practical to analyze, do you know any other formulas that would produce useful results through an analysis of them?

[deleted-2574]

Hi gogopoco,

Some websites with formulas are:

http://www.ma.utexas.edu/users/kawasaki ... form1.html
http://engr.astate.edu/jdg/Circuits/Lab ... mulas.html (for Electric Circuits)

Do these help?

[deleted-2574]

Hi gogopoco,

Heron's Formula is useful, it can be used to calculate a triangle's area knowing only the lengths of the sides.
For example, in the classic right triangle with sides of lengths:
3, 4, 5

Heron's formula says the area of the triangle (here sides a, b, c) is:

SQRT(s*(s-a)*(s-b)*(s-c)), where SQRT is the square root and
s is the semiperimeter of the triangle: (a+b+c)/2
In the 3,4,5 triangle, s = (3+4+5)/2 = 6

According to Heron's formula the area of the triangle is:
SQRT(6*(6-3)*(6-4)*(6-5))=SQRT(6*3*2*1)=SQRT(36)=6

The other way of computing the area is:
since the triangle has sides 3, 4, 5, it is half of a rectangle with sides 3 and 4. The area of the rectangle is 12 (3*4). The area of the triangle is 6.

So both ways of computing the area match!