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## #1 2012-07-23 00:22:09

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,845
Website

### Heron's Formula

We have a school project on The Applications Of Heron's Formula
It has to contain a minimum of 5 pages apart from the introduction
I replace 1 of them with the proof.
Please show me how can I prove it
And in the other 4 pages we have to show various Applications of the Formula
Could you suggest some of them

P.S.: Please give a proof without any Trigonometry and pls don't recommend that which is given in Wikipedia because I didn't understand it

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #2 2012-07-23 00:25:25

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

### Re: Heron's Formula

Hi Agnishom

You could put an example on one page. An application on a quadrilateral on another.

Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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## #3 2012-07-23 00:46:24

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,845
Website

### Re: Heron's Formula

So I can fill 2 of the 4 pages: 1 with a simple example & the other with an example on Quadrilateral
Please give two other applications( May be two interesting problems)

I don't understand what's written on Wikpedia

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #4 2012-07-23 01:42:05

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

### Re: Heron's Formula

I have to say that don't remember. I will read the Wikipedia article and then try to explain it to you.

Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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## #5 2012-07-23 03:06:09

noelevans
Member
Registered: 2012-07-20
Posts: 236

### Re: Heron's Formula

It's kinda interesting that the formula lets you know whether or not you have a legitimate triangle.
If it gives zero then it indicates that you have a "pretty doggone flat triangle."  Eg. 4,5,9.
It gives a negative number under the radical when it can't be a triangle.  Eg. 4,5,10.

Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional).
LaTex is like painting on many strips of paper and then stacking them to see what picture they make.

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## #6 2012-07-23 03:11:47

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

### Re: Heron's Formula

Hi Agnishom

Which of this don't you understand:

Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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## #7 2012-07-23 03:28:54

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,845
Website

### Re: Heron's Formula

I wrote:

I required a proof without trigonometry

Anyway, this did help:

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #8 2012-07-23 03:35:08

bob bundy
Registered: 2010-06-20
Posts: 8,228

### Re: Heron's Formula

And in the other 4 pages we have to show various Applications of the Formula

Well, you can work out the area of a triangle when you know its sides.

I will see if I can find anything else.

Proof without trig?  That may be a tough request to fulfil.

The first post on that site using the trig formulas.

The second takes a huge leap un-proved.  I have a suspicion that trig will be involved there too.

I've know of a book with a proof but it'll be 24 hours before I can look it up.  (and I seem to remember it has trig too)

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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## #9 2012-07-23 03:50:56

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,845
Website

### Re: Heron's Formula

No I can understand it the way it is proved using Pythagoras

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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