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Science Forum Index » Physics Forum » The tangent line must touch two points
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| Robert J. Kolker |
 Posted: Thu May 01, 2008 7:24 pm |
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mitch.nicolas.raemsch@gmail.com wrote:
Quote: In order to derive a tangent line on a changing curve you must do
calculus. You must pick two points to get the the tangent line and get
the same slope. Calculus is just an estimation. You cannot become
infinitely accurate because you cannot make infinite calculations. You
could make a million!
Review the limit concept and rethink the matter.
Bob Kolker |
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| Ralph Hertle |
| Posted: Fri May 02, 2008 12:15 am |
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mitch.nicolas.raemsch@gmail.com wrote:
Quote: On May 1, 1:25 pm, tadchem <tadc...@comcast.net> wrote:
On May 1, 4:09 pm, mitch.nicolas.raem...@gmail.com wrote:
In order to derive a tangent line on a changing curve you must do
calculus. You must pick two points to get the the tangent line and get
the same slope. Calculus is just an estimation. You cannot become
infinitely accurate because you cannot make infinite calculations. You
could make a million!
Mitch Raemsch
You are pushing my patience to the infinitesimal limit...
Tom Davidson
Richmond, VA
In order to be precise calculus must make infinite calculations.
Mitch:
That is impossible. It is impossible to create a particular number or
finite location for what is claimed to be the infinite.
You need to read the several posts, excerpts, and replies that I have
posted to HPO, alt.sci.physics, and other Usenet NGs during the last
several years. You will find discussions regarding the claimed concept
of 'infinity' and also regarding the concepts of the 'continuity' of
objective existence and on the continuity of the functioning of
universal concepts.
The Platonic (anti-) concept of 'infinity' requires non-factual
definitions. Properly, science requires definitions that precisely
identify the facts of existents and factual relationships in the universe.
Religio-infinitism requires the ignorance of the concept of the
continuity of existence in the universe, and, also, of the universality
of concepts that identify and logically demonstrate the facts of existence.
The clash is between the concepts of 'infinity of number' that is
contrary to the 'continuity of existence and principle'. The latter is
true, and the former is not.
The issue involved with the Calculus is a simple matter of the
incommensurability of the entities of the calculus curve, say, a circle,
and that of a triangle. Change to circular coordinates, or to the
functional coordinates of B-spline curves and its a different game.
If a sphere is modeled within a spherical coordinate system the
continuous and universal principle of the sphere would generate a
surface or volumetric solid, or for that matter, an Archimedes mass
value. Similarly the entity, say a triangle, modeled in 2D orthogonal
coordinates, would be identified as having a continuous principle of
functioning, or function, within certain selected limits.
Precision, is a function of the definitions involved. If Platonic, and
Heisenbergian, unknowable definitions are employed no precise
calculation demonstration is possible.
The answer to the dilemma is to get rid of the anti-concept of infinity
everywhere it is used, and to rely upon the concepts of the continuity
of the existence of the universe and the identified laws of the universe.
BTW: a straight line that cuts or touches a curved line at (at least)
two points is a chord. A tangent is a straight line that does not cut
the curved line and that touches the curved line at only one point. The
premise of the subject line of this thread is scientifically incorrect,
and it is self -contradictory. No true scientific conclusions may be
drawn from it.
Ralph Hertle |
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