Analysis puzzle

[davieddy]

Originally Posted by mfgoode

"Shearing transformation"? Ha! ha ! Ha!
Mally

Do you find my pwoposition wisible?

[mfgoode]

Originally Posted by davieddy

Do you find my pwoposition wisible?

It will be of interest to take statistics on how many of your 301 posts are one liners 50% of which are nonsensical. Reminds me of another old timer but at least he has the disadvantage of English being a second language to him

Any way Teacher dont be dismayed as I quite enjoy them.

From Mally the preacher

[99.94]

Originally Posted by davieddy

Do you find my pwoposition wisible?

The Life of Brian? (Topical for Easter).

[Orgasmic Troll]

Originally Posted by mfgoode

It will be of interest to take statistics on how many of your 301 posts are one liners 50% of which are nonsensical. Reminds me of another old timer but at least he has the disadvantage of English being a second language to him

Any way Teacher dont be dismayed as I quite enjoy them.

From Mally the preacher

Is this the pot calling the kettle gray?

[davieddy]

Originally Posted by TravisT

Is this the pot calling the kettle gray?

Don't knock my mate Mally: he makes me feel young again

[mfgoode]

Originally Posted by Orgasmic Troll

Is this the pot calling the kettle gray?

In the words of the song 'Fever': "There is a fire below, down below, in my heart!"

Another way of putting it. 'When you have snow on the roof it doesn't mean there is no fire in the hearth'

Mally

[davieddy]

I think by "gray" he was referring to the lack of clarity in our
posts; not the colour of our hair

David

[mfgoode]

Thanks Dave. I'm relying on you to interpret tricky one liners!

Mally

[davieddy]

Originally Posted by Kees

Finally I found something. Well, to be more precise, Archimedes found something.
Take two points A, B on a parabola and let the tangents to the parabola at A and B intersect
at S. Then the area enclosed by the chord AB and the parabola is 2/3 of the area of the triangle ABS. The area which we are considering is the complentary 1/3 part of the triangle.
So the question can transformed to the question of finding the set of all such triangles with constant area.
Have not worked out the details yet, but this seems a good way to start.

If S is at (X,Y) let X² - Y = a².
If we can show that the x coords of A and B are X-a and X+a,
and the mid point of AB lies at y coord Y + 2a²,

the area of the triangle ABS is 2a³.

This led me to my "shearing" proof of these results (in my head),
considering the case of S at (0,-a²).

It also follows that AB is parallel to the tangent at x=X.

David