Elipse

Elipse (pg. 117-130)

X2+y2=1 y2+x2=1
a2 b2 a2 b2


Hoy seguimos viendo el tema de la elipse haciendo los problemas 9 y 11

9.- 2x^2 + 3y^2 = 12

En este tipo de problemas tenemos que dividir toda la ecuacion por 12 para que asi nos de formula comun:

2x^2 + 3y^2 = 12
12 12 12

1x2 + 1y2 = 1
6 4

x^2 + y^2 = 1
6 4

ya teniendo la ecuacion sacamos a2 b2 y c2 a,b y c

a2=6 a=,/6
b2=4 b=2
c2=2 c=,/2

ahora se sustituiran estos valores en las formulas

V(a,0) F(c,0) b(0,b) y Ep

luego se grafica

Archimedes (287-212 B.C) was the greatest mathematician of the ancient world. He was born and lived in Syracuse, a Greek colony on Sicily, a generation after Euclid.
He is said to have used parabolic mirrors to concentrate the rays of the sun to set fire to Roman ships attacking.

King Hieron II of Syracuse once suspected a goldsmith of keeping part of the gold intendend for the King´s crown and replacing it with an equal amount of silver.
The king asked Archimedes for advice. While in deep thought at a public bath, Archimedes discovered the solution to the king´s problem when he noticed that his body´s volume was the same as the volume of water it displaced from the tub. As the story is told, he immediately ran home naked shouting “Eureka, eureka!” [ “I have found it, I have found it”!].
This incident attest to his enormous powers of concentration. In spite of his engineering prowess, Archimedes was most proud of his mathematical discoveries. These included the formulas for the volume of a sphere, V= 4/3 ii r 3 ; the surface area of sphere, S= 4 ii r 2; and a careful analysis of the properties of parabolas and other conics.

opinion

Archimedes era un griego matematico(was an ancient Greek mathematician, physicist, engineer, astronomer, and philosopher. He is widely regarded as the most important scientist in antiquity. Carl Friedrich Gauss, himself frequently called the most influential mathematician of all time, stated that Archimedes was one of the three epoch-making mathematicians, with the others being Sir Isaac Newton and Ferdinand Eisenstein.) Archimedes dio una gran aportacion a las matematicas descubriendo las formulas de la esfera y analizando las secciones conicas

El tema de la elipse no tiene nada de complicado, pueda ser que este laborioso y que tenga varios pasos y formulas pero en realidad es solo sustituir los valores y hacer las operaciones algebraicas y luego graficar correctamente