Re: A SIMPLE CHALLENGE that you great Mathematicians won't answer...

On Feb 12, 6:16 pm, finite guy <adamle...@xxxxxxxxxxxx> wrote:
On Feb 13, 4:07 am, bill <b92...@xxxxxxxxx> wrote:



On Feb 11, 6:08 pm, finite guy <adamle...@xxxxxxxxxxxx> wrote:

Consider a circle: x^2 + y^2 = c

To construct a 'perfect mathematical circle'
requires delta x and delta y to BE zero
from point-to-point in the circle -
not just 'approach zero'.

If delta x and delta y have ANY magnitude
from point-to-point then the 'circle' is a polygon.
It is irrelevant as to how many sides the polygon has -
it could be a billion^billion facets
but it will still be a polygon.

If delta x and delta y are allowed to be zero
from point-to-point in the 'circle'
then we are discussing one point only - not a circle.

How do you try to explain this obvious situation????

Not being a great mathematician, I
don't understand why delta x and
delta y have to be zero. Can you
explain why this is necessary?

TIA,

Bill J- Hide quoted text -

- Show quoted text -

Easy.
If they are not zero from point to point
- then discrete, straight line lengths are expressed between points -
no curve.
This in turn makes the circle not smooth but a polygon.

By extension, nothing 'curves' as such - but it is possibly nearly
smooth to our 'eye'.

Why do the lines between points have to be straight lines?
Theoretically there can be NO line; because a line conists
of more points!

Originally, I was thinking of delta x & y as the x- & y-distances
between two points on a curve. Back in my academic youth
(circa 1945 -1956) we had dx & dy which had something to do
with delta -x, -y This should help explain my confusion!

Bill j

Curves and graphs are a useful tool for visualisation but can never be
smooth.
This applies to all possible 'powers' .

Harder - but still easy.
Fermat said:
It is impossible for a cube to be written as the sum of two cubes or a
fourth power to be written as the sum of two fourth powers or, in
general, for any number which is a power greater than the second to be
written as a sum of two like powers.

The philosophy of current mathematics neglects the implications of
this.
Mathematicians, Fermat excluded,
don't understand that a 'cube' is a 4th power entity - not a third
power one.

If you check Fermats phrasing you will see that he uses inconsistent
terminology.
He omits to say 'third power' anywhere but uses the venacular 'cube'.
It is a semantic trick by Fermat.

It is impossible for a cube
to be written as the sum of two cubes
or [IN OTHER WORDS]
a fourth power
to be written as the sum of two fourth powers

or, in general,
for any number
which is a power greater than the second
to be written as a sum of two like powers.

a^3 + b^3 = c^3
The mathematicians here will readily agree that you cannot construct a
c^3.
They fail to realise that it is impossible to make the a^3 or the b^3
in the first place...
There is no cube, or other 'spatial' entity in 3 powers.
It takes 4. And there are no more.

They don't even appreciate why E=mc^2 is a planar relationship - not
'spatial'.
The original Pythagoras Theorem is conceptually flawed.

Send me an email, I'll send you a powerpoint.

.

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