Nicolas Copernicus

Matthew Brown

Ma 330-001

April 1, 1999

Works Cited

Boyer, Carl. A History Of Mathematics , Second Edition, John Wiley & Sons Inc.:1991, p 291.

Burton, David. History Of Mathematics , Third Edition, Wm. C. Brown Publishers Inc.:1995, p 312-313.

(www 1). http://history.math.csub.edu/Mathematicians/copernicus.html.

(www 2). http://www.bo.astro.it/copernicus/cop-eng.html.

Nicolaus Copernicus was a Polish astronomer who contributed a great deal to the area of astronomy. He was born in 1473 in eastern Poland, where he was the son of a merchant. Copernicus entered the University of Crakow, where he became interested in the field of astronomy (www 1). "In 1497, he was sent by his uncle to study at the University of Bologna, where he also studied Greek language, mathematics, and the writings of Plato (www 2)." Copernicus studied the Ptolemaic system of astronomy, which was a geocentric idea or an idea that the earth was the center of the universe and everything else revolved around it. "As conceived by Aristotle and elaborated by Ptolemy, this system placed the earth at the center; and then at increasing distances from it came nine crystalline and concentric spheres. The first seven spheres carried the sun, the moon, and the five known planets, and fixed stars were attached to the eighth one, often called the firmament . An elaborate theory of epicycles, deferents, equants, and eccentrics accounted for each planet's motion within its own sphere. On the outside lay the ninth sphere, known as the primum noble representing the Prime Mover, or God. Beyond this last sphere, there was nothing, no matter, no space, nothing at all (Burton 312)." The more Copernicus studied the Ptolemaic system, the more dissatisfyied he became. Through more in depth study, Copernicus found evidence that the Sun was in fact the center of the universe. "In the new cosmology produced by Nicolaus Copernicus, the sun changed places with the earth; the sun became the unique central body and the earth merely one of several planets revolving about the stationary sun. Copernicus' theory changed the nature of the universe from a goecentric belief to a heliocentric or Sun-centered belief, and the planets, including the Earth revolve around the Sun. Even with factual evidence to prove his theory Copernicus could not openly present his findings, because they went against the ideas of the Bible and the Pope at the time. The theory of having the earth move around the sun conflicted with certain passages in the Bible. The 93rd Psalm states, "He hath made the round world so sure, that it cannot be moved." As a result of Copernicus' theory, a divide was created between science and religion, and Copernicus did not openly promote his findings. "From about 1510 to 1514, Copernicus prepared a short manuscript to summarize his new idea, De hypothesis motrum a se constitutis commentariolus , which he privately distributed among friends in 1514 (www 2)." In this manuscript, Copernicus summarized that the Earth was not the center of the universe and revolved on its axis around the sun. He supported this claim with diagrams and mathematical calculations, and it was not until 1536 when he was given permission by Pope Clement VII to even publish his findings. In 1543, the year of his death, Copernicus published a book of all of his findings entitled, De Revolutionibus Orbium Coelestium . However there was still a divide between the geocentric people and those who accepted the Copernican heliocentric theory. "Copernicanism was so incompatible with the traditional interpretation of various passages in the Bible that if it should prevail, it seemed that the Bible would loose authority, and Christianity would suffer (Burton 313)." It was not until after Copernicus' death when another astronomer by the name of Galileo Galilei continued where Copernicus left off.

Heliocentric Model of the Universe

> with(plottools);

> with(plots);

> sun := disk([0,0,0],.9,color=yellow):

> mercury := t->disk([1.1*cos(2*Pi/87*t),1.1*sin(2*Pi/87*t)],.03,color=brown):

> venus := t->disk([1.35*cos(2*Pi/225*t),1.35*sin(2*Pi/225*t)],.07,color=pink):

> earth := t->disk([1.75*cos(2*Pi/365*t),1.75*sin(2*Pi/365*t)],.1,color=blue):

> mars := t->disk([2.1*cos(2*Pi/687*t),2.1*sin(2*Pi/687*t)],.08,color=red):

> jupiter := t->disk([3.1*cos(2*Pi/4329*t),3.1*sin(2*Pi/4329*t)],.65,color=turquoise):

> saturn := t->disk([4.5*cos(2*Pi/10753*t),4.5*sin(2*Pi/10753*t)],.5,color=violet):

> uranus := t->disk([5.5*cos(2*Pi/30667*t),5.5*sin(2*Pi/30667*t)],.31,color=magenta):

> neptune := t->disk([6.3*cos(2*Pi/60148*t),6.3*sin(2*Pi/60148*t)],.33,color=gold):

> pluto := t->disk([7.3*cos(2*Pi/90520*t),7.3*sin(2*Pi/90520*t)],.31,color=grey):

> drawit :=t -> display([sun,mercury(t),venus(t),earth(t),mars(t),jupiter(t),saturn(t),uranus(t),neptune(t),pluto(t)],scaling=constrained,axes=none):

> drawit := proc (t) options operator, arrow;
display([sun, mercury(t),venus(t),earth(t),mars(t),jupiter(t),saturn(t),uranus(t),neptune(t),pluto(t)],scaling = constrained,axes = none) end:

> display([seq(drawit(10*i),i=0..40)],insequence=true,scaling=constrained);

Geocentric Model of the Universe

> geocentric := plots[display]([
disk([0,0],1,color=blue),textplot([0,0,`Earth`],color=white),
disk([0,0],2,color=white),textplot([0,1.5,`Moon`]),
disk([0,0],3,color=brown),textplot([0,2.5,`Mercury`],color=white),

> disk([0,0],4,color=pink),textplot([0,3.5,`Venus`]), disk([0,0],5,color=yellow),textplot([0,4.5,`Sun`]), disk([0,0],6,color=red),textplot([0,5.5,`Mars`],color=white),

> disk([0,0],7,color=green),textplot([0,6.5,`Jupiter`]),

disk([0,0],8,color=magenta),textplot([0,7.5,`Saturn`],color=white),

> disk([0,0],9,color=tan),textplot([0,8.5,`Firmament`]), disk([0,0],10,color=cyan),textplot([0,9.5,`Crystalline`]), disk([0,0],11,color=gold),textplot([0,10.5,`Heaven`])],axes=none,scaling=constrained):

> geocentric;

>

Conclusion

Copernicus' discovery of a heliocentric universe was indeed a great discovery. However, with change there are those who do not accept change so readily. In this case Copernicus' discovery of a heliocentric universe was criticized by those who held strong to the Ptolemiac system of a geocentric universe. It was not until after Copernicus' death that his theory was accepted by the church and the government. "Most of us today think of Nicolaus Copernicus as an astronomer who revolutionized the world view by successfully putting the earth in motion about the sun; but an astronomer is almost inevitably a trigonometer as well, and we owe Copernicus a mathematical obligation as well as an astronomical debt (Boyer 291)."