WHETHER MATHEMATICS is GUILTY THAT ROCKETS FALL? WHETHERare GUILTY MATHEMATICS THAT ROCKETS FALL?
Recently our rocket production is not lucky for some reason, there were mass cases of loss of the satellites launched in space what report us mass media about. And the reason cannot be defined. Roofing felts commercialization of space programs exerts such impact. Roofing felts all experts retired, and new cannot work yet as it is necessary. Only our spaceships in increasing frequency fall.
Reason of unsuccessful start of the carrier rocket “ Proton “ with three GLONASS satellites onboard experts consider mistakes in software. The mathematician will be fired now, and as it often happens, will close office and begin to be created new, on new technologies. And whether there are they - these technologies and whether mathematics is guilty of drawing up the calculations till this day not clearly.
In this case the mathematician can be personally not guilty of falling of the rocket though the mistake in calculations more than is probable. The mistake was made not today, and many years ago when solved one of the most popular mathematical tasks, about a circle quadrature, i.e. about construction by means of compasses and a line of a square, to equal this circle.
If to designate circle radius through r, then it will be a question of creation of a square which area is equal π r2, and the party is equal to r. Now it is known that number π - the circle relation to the diameter - number irrational. It is expressed by recurring acyclic decimal decimal 3,1415926 …, and was, is calculated with 707 decimal signs the mathematician V. Shenks. He published this result together with a formula of calculations in 1837.
Under the words “ Circle Quadrature “ understand as a problem of exact creation of a square, equal to a circle, and a problem of calculation of the area of a circle with this or that approach. The problem about an exact quadrature of a circle was tried to be solved originally with the help of compasses and ruler. The attempts of the solution of a task on a circle quadrature continuing during the millennia steadily terminated in failure.
Since 1775 the Parisian Academy of Sciences, and then and other academies began to refuse consideration of the works devoted to a circle quadrature. In the 19th century scientific justification of this refusal was given: unsolvability of a quadrature of a circle by means of compasses and a ruler is strictly established.
At the end of the 18th century the German mathematician I. Lambert and the French mathematician A. Legendre established irrationality of number π. In 1882 the German mathematician F. Lingdemang proved that number π (so i) it is transcendental, that is does not satisfy to any algebraic equation with the whole coefficients. Lingdemang`s theorem put an end to attempts of the solution of a task on a circle quadrature by means of compasses and a ruler.
So, number π transcendentally - it is the number equal to the circle length relation to length of its diameter, its brought closer value is equal to 3,1415926... And there is an absurd situation when “ quadrature “ the tasks proved by number π are declared not solvable, and at the same time the official mathematics uses formulas with the same number as officially recognized for calculations.
It became clear that by results of Lingdemang`s theorem, today we have no tool to calculate the area of a circle. Is transcendental π which is used till this day, and there is no constant which has to be the second area of a circle, komponenty for calculation. And it contradicts mathematical rules of creation of geometrical figures which have to be under construction with application concrete and constants. So illegal was the formula of calculation of the area of a circle based on transcendental numbers.
And there is a thought. And suddenly this place is not taken yet and nobody after tasks “ forbade “ did not calculate the necessary numerical value - a constant for creation of a circle? The logic speaks, time calculated transcendental size, it is possible to calculate also a constant. A little possibly, but as they say in such cases, you never can tell. We build a rectangular triangle with the parties 10 and 10 and we measure its hypotenuse.
So: The root square of 200 is necessary, but for the lack of the necessary calculator or Bradis`s tables the root is calculated approximately to 4 - y figures after zero, using a notebook in a cage and a ruler = 14. 1422.
Further we calculate radius: 14. 1422:10 × 4=5. 65688; then r ² =5. 65688 × 5. 65688=32. We calculate 000291
" From here; constant “: 100:32. 000291=3. 12497
So: The constant necessary for creation of a circle is found =3,12497
Check: 32. 000291 × 3. 12497=99. 9999
we Repeat calculation and we will take other rectangular triangle with the parties 11 × 11; We Calculate a hypotenuse and we find radius: 15. 55:10 × 4=6. 22; 6. 22 × 6. 22 × 3. 12497=120. 900;
at the same time 11 × 11=121.
We will repeat experiment once again and we will take the following rectangular triangle with the parties 12 × 12; We Calculate a hypotenuse and we find radius: 17:10 × 4=6. 8; 6. 8 × 6. 8 × 3. 12497=144. 49;
at the same time 12 × 12=144.
we Remove a formula Skp. = π territory of r ²; where Skp. - area of a circle; π the territory - Pythagoras`s constant (we will pay tribute to the founder of mathematics); r- circle radius.
We check calculations with an old and new formula on a square with the parties 10 × 10
Use of a formula Skp. = π r ²: External radius: 7. 0711 × 7. 0711=50. 00 × 3. 14=157
Apothem: 5 × 5=25. 00 × 3. 14=78. 5
Use of a formula Skp. = π territory of r ²: External radius: 7. 0711 × 7. 0711=50. 00 × 3. 12=156
Apothem: 5 × 5=25. 00 × 3. 12=78. 00
Consequence: Two systems of the equations are called equivalent if these systems have the same decisions.
Consequence: If to replace each equation of system with the equivalent equation, then the system equivalent will turn out this.
Conclusion: Constant π the territory conforms to requirements of geometry for creation of figures. While number π tratsedentno and in creation of exact figures it should not be used.
Because a difference between the π variable; =3. 14 and the constant calculated by us π territory = 3. 12 makes 0. 02 that in calculations of this distortion are almost not visible. The result of a deviation can affect only at calculation of big orbits and trajectories when, for example the rocket which does not have additional to settlement (at economy of fuel) a power stock can not reach the necessary flight altitude. The way of construction " will be shown in the following article; not solvable “ tasks.
The above described calculation says that it is impossible to accuse the mathematician that it made a mistake when there is no exact tool for check of its work. Mathematics is not guilty that they in the calculations use “ wrong “ formulas.