A lgebraic solution to a geometric problem. S quaring of a lune. Even in ancient times people have watched and studied the dependence of the moons and their daily lives.
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
Squaring of a lune
By the Pythagorean theorem
midpoint D of AC.
Small semicircle = 1/2 large semicircle.
Excavations in Baylovo
= m.Q 1= n Q
m= 2 n= 1
m= 3 n= 1
m= 3 n= 2
m= 5 n= 1
m= 5 n= 3
, b = sin 1
In 1902 E. Landau deals with the question of squaring a moon. He proves that the moon can be squared of the first kind Numbers
If the number of c= 0 is squarable moon, and if the corners are not commensurate Moon squarable. It is believed that he used the addiction, which is familiar and
a gaussian number in which the moon is squarable. When k = 1, k = 2 are obtained Hioski cases of Hippocrates.
Х8 + Х 7 - 7Х6 + 15Х4 +10 Х3 – 10Х2 – 4Х + 1 -
In 1929 Chakalov Lyubomir (Bulgarian mathematician) was interested of tLandau’s work and used algebraic methods to solve geometric problems. Chakalov consider the case p = 17, making X = cos 2 and obtained equation of the eighth grade.
+ sin 2
Chakalov use and another equation
n Xn ( Xm - 1 )2 – m Xm ( Xn – 1 )2 = 0
X = 1 is the root of the equation
So he gets another equation:
A. C. Dorodnov had proven cases in which polynomial of Chakalov is broken into simple factors and summarizes the work of mathematicians who worked on the problem before him. So the case of clauses is proven.
SOU “Zheleznik” Bulgaria