However, we cannot directly measure pi according to the definition of pi. Because the circumference and diameter of a circle cannot be measured very accurately, it is impossible to get an accurate value of pi.
So, how is pi obtained?
At first, mathematicians used the tangent circle method to calculate pi. By making the positive inscribed polygon and the positive circumscribed polygon of the circle, the more sides are made, the closer the regular polygon is to the circle. By calculating the side length or area of a regular polygon, the upper and lower bounds of pi can be calculated. 1500 years ago, Zu Chongzhi, a mathematician in China, used this method to accurately calculate the first seven decimal places of pi, which was one thousand years earlier than the world.
Since then, mathematicians have found that pi can be expressed by infinite series, and the commonly used formulas are:
The more terms are calculated, the more accurate the pi is. At present, human beings have calculated the first 365,438+0.4 trillion decimal places of pi by using infinite series with very fast convergence rate and computer. But pi has not been counted in the end, and who is the last one is unknown.
So, can pi be calculated?
Although the circumference and diameter of a circle exist, neither of them can be rational numbers at the same time. Mathematicians have proved in many different ways that pi is endless, its decimal place is infinite and acyclic, and it is an irrational number. So the circumference and diameter of a circle have only one rational number at most. For example, the diameter of a circle is 1 and the circumference is? ; The diameter of the circle is 1/? , the perimeter is 1.
In addition, pi is not only inexhaustible in the decimal system. Actually, except n? The pi of decimal and other decimal systems is also irrational. It can be said that this property of pi is a basic property of our cosmic space-time. If there is an alien civilization in the universe, the same conclusion will be found.
Although pi is not the last one, what will happen if pi is calculated? Will the circle still exist? What will happen to the universe we live in?
In this case, an absolutely smooth curve does not exist, and the circle is not completely smooth. They are actually composed of regular polygons with finite sides. By secant, the circle can be divided to the end.
Pi is a rational number, which will bring a huge problem that calculus will not be established and the formulas related to calculus are all wrong. The existing mathematical axiom system is wrong, and there are huge loopholes in the strict logic of mathematics. The mathematical building built by mankind for thousands of years will collapse. On the other hand, it will open a golden age of mathematics, and there will be a broader? Mathematical continent? Be discovered.
The change of pi will profoundly affect our universe, because our present universe exists on the premise that pi is unreasonable. If pi becomes a rational number, the nature of space-time will change, and various constants and physical laws in the universe may also change, which may even lead to the formation of the universe.
Of course, in our universe, pi cannot be proved to be a rational number. Mathematics is not like physics. Physical constants need to be based on measurement (the defined vacuum light speed is considered to be special), while mathematical constants are completely determined values and can be strictly deduced logically. The complete calculation of pi can only happen in other parallel universes (if parallel universes exist), and the physical laws of that universe are completely different from ours.