The Geogebra materials are now located at:

Also a link is provided on the new calculus page:

A couple of days ago, the directors of Geogebra decided to remove my materials from GeoGebraTube and terminate my account. In fact, there was no problem with the materials but they found an excuse in the language I had used in my comment.  Of course, this is all they needed. Not for one moment can anyone believe they actually cared about the comments! The real reason was that they wanted any excuse to remove the materials which expose academic ignorance and stupidity. 

This is the kind of society they live in – one in which ideas are censored or banned completely. These individuals believe that you are incredibly stupid and that you can’t think for yourselves! So they terminated my account for YOUR own good, Well, if you believe this, then you are even a bigger idiot than I imagined.

First it was ResearchGate (RG) that banned my account, then Weebly (has since rescinded its ban) and now GeogebraTube. So who will be next?  

A really funny story about RG, is that one of their members was a confined psychiatric patient!  They did not know about this until I pointed it out to them and even then, it took them weeks to realize a psycho was commenting on their “scientist” boards. 

If I am such a fool and a crank and a psycho or whatever else, how is it that these and other organizations go to such lengths to silence my ideas? They KNOW I am correct and that they are morons. Of course they can’t acknowledge my work, because once they do, they have confirmed their ignorance, stupidity and incompetence. I don’t know which is worse, the academic bourgeoisie or the Catholic church…  I suppose the inquisitors might have learned a few tactics from these modern Nazis.

I had a debate with an unbelievably stupid American Jew some years ago – one called Mark Chu Carroll.  (

“You can’t traverse that subtree to infinity! You just can’t” claimed Carroll. 

and in the next breath:

“1/3 = 0.333…”

Well, the crank no longer accepts comments on his blog but the following link refutes the idea that real numbers are well defined:

And the following link provides a proof for simpletons that 0.999… is NOT equal to 1:

The fallacy that 1/3 = 0.333… is debunked, and hence the claim that 0.999… and 1 are the same falls.

The Swiss mathematician Euler erred gravely in reaching his conclusion that 0.999… = 1. Euler failed to realize that by definition, 0.999… must be less than 1. So why did he fail in this regard?

The answer becomes evident when one realizes that Euler was among the first mathematicians to start treating all mathematical objects as numbers without paying detailed attention to the attributes and definitions of the same.

Euler incorrectly assumed that the ill-defined quasi-number concept of 0.999.. is a number, and applied some of the number theorems he already knew, to reach (erroneous) conclusions regarding its equivalence to 1.

He was famous for being a proponent of quasi-number objects, for example, the complex “numbers”. Euler is associated with many ill-defined concepts that include complex numbers. One well-known ill-formed identity is the equality relating pi, sqrt(-1), -1 and e. In truth, none of these concepts except -1, are well-defined.

Since Euler, many modern mathematicians have succumbed to these erroneous and toxic ideas.

Perhaps I should not be too critical of Euler because his introduction of function notation was a great contribution to mathematics.

1. Area is the product of two averages.
2. Volume is the product of three averages.
3. Hypervolume in n dimensions is the product of n averages.

1. A point is:
a. the idea of location or place.
b. the foundational geometric object.
c. the object from which all other geometric objects are defined.
2. Distance is the idea of proximity.
2. Path describes the distance between any two points.
3. Between any two points, there are infinitely many paths.
4. The measure of distance is called length.
5. The path with the least length between any two points is called a straight line.
6. Area is the idea of surface.
7. A plane is a flat area.
8. Given any magnitudes, an average is that value each of the magnitudes would
have if they were equal or made to be equal.
9. Straight lines in a plane which never meet even if extended indefinitely at either end,
are called parallel lines.
10. A geometric object whose opposite sides are equal and parallel is called a parallelogram.
11. For any parallelogram, the average length of the lengths of infinite parallel lines it contains, is
equal to one of its sides.
12. A triangle is a geometric object described by the shortest paths joining three points in a plane.
13. The point at which two planar lines meet or intersect in a plane is called a vertex or corner.
14. An angle is the idea of orientation or inclination between two intersecting planar lines from
their vertex in the plane.
15. If two planar lines cross each other in a plane forming four equal angles, then each of these
angles is called a right angle.
16. Any triangle that contains one right angle is called a right angled triangle.
17. The side of greatest length in a right angled triangle, is called a hypotenuse.
18. A diagonal is a line that cuts a parallelogram in two identical triangles.
19. Any parallelogram whose sides all meet at right angles is called a rectangle.
20. The diagonal of a rectangle is the hypotenuse of the two right angled triangles.
21. The shortest length between the diagonal end points of a rectangle is the diagonal.
22. Comparison of parallelogram areas is called rectangular area measure.
23. For any right-angled triangle it can easily be proved that the square on the hypotenuse is
equal to the sum of the squares formed on the remaining two sides of the same triangle.
24. The shortest length between any two points in a plane can be indirectly described by the
square of the hypotenuse length, if these points are the endpoints of the hypotenuse.

1. A magnitude is the concept of size or dimension.
2. The comparison of any two magnitudes is called a ratio.
3. A ratio of two equal magnitudes is called a unit.
4. A magnitude that is completely measurable by another magnitude is a rational ratio of
5. A rational ratio in which the antecedent and consequent magnitudes are related as
factor/multiple or multiple/factor, is called a number.
6. Any magnitude that is a multiple of a unit is called a natural number.
7. Zero is the idea of no magnitude.
8. A fraction is a ratio of two numbers.
9. If for any ratio, one magnitude is an exact multiple of the other, then such a ratio is a fraction if
and only if, each of the magnitudes are multiples of a unit.
10. If any magnitude or ratio of magnitudes cannot be completely measured, then it is called an
incommensurable magnitude or ratio of magnitudes.

1. A symbol represents a magnitude.
2. An expression is given in terms of magnitudes and symbols.
3. An algebraic difference is the comparison of two expressions.
4. Two expressions are equal if their algebraic difference is zero.
5. An equation is formed from two equal expressions.
6. An inequality is formed from two unequal expressions.
7. The difference of zero and any expression is the expression.


1. The difference (or subtraction) of two magnitudes is that magnitude which describes how
much the larger exceeds the smaller.
2. The difference of equal magnitudes is zero.
3. The sum (or addition) of two magnitudes is that magnitude whose difference with either of the
two magnitudes is either of the two magnitudes.
4. The quotient (or division) of two magnitudes is that magnitude that measures either magnitude
in terms of the other.
5. If a  unit  is divided by a magnitude into parts, then each of these parts of a unit, is called the
reciprocal of that magnitude.
6. Division by zero is undefined.
7. The product (or multiplication) of two magnitudes is the quotient of either magnitude
with the reciprocal of the other.
8. The difference of any magnitude and zero is the magnitude.

Observe that all the basic arithmetic operations are defined in terms of difference.

(*) It is only possible to measure magnitudes by comparing the same qualitatively or quantitatively, that is, the prior definition of difference is mandatory.


An  average  is the value that results when a given set of data or observations are made to be equal either through re-distribution or by some other method.

A  natural average  is an average of an infinite set of continuous data, which is possible because of the Mean Value Theorem. The New Calculus is based on the theory of Natural Averages.