1. “The greatness of a population is measured by the ideas it owns."

2. The big difference between Hellenistic science and previous science is the introduction of the scientific method. It has allowed the achievement of a technological level equal to that of 17 th -century Europe.

3. Integrals Archimedes of Syracuse (Syracuse, 287 b.C. – Syracuse, 212 b.C.), a mathematician, an engineer, a physicist and an ancient Greek inventor (Siceliot), was one of the greatest scientists of history.

4. Greek «Pi» is a mathematical constant which is indicated with, which is used a lot in science. Since antiquity a lot of civilizations have tried to define its value. Babylonians = 3… But it’s by defect! Egyptians 2 =3,160… But it’s by excess!

5. Archimedes understood that the measurement of the circle was comprehended between the perimeters of an inscribed and a circumscribed polygon. The more sides the polygons have, the closer one gets to the exact value of. Let’s imagine a circle whose diameter equals 1 and two squares, one inscribed and another circumscribed. The perimeter of the inscribed square is 4. = 2,828. The perimeter of the circumscribed square is 4 · 1= 4, therefore 2,828 < < 4 S = 1 C= If we consider an inscribed and a circumscribed hexagon… … 3,0< < 3,21539

6. Then Archimedes progressively doubled the sides of the two polygons up to two 96-side polygon. He noticed that the more sides the polygons had, the more defined the value of … Today we know that… … 3,140 < < 3,142

11. Number of sides Side measure of the inscribed polygon Side measure of the circumscribed polygon Perimeter of the inscribed polygon Perimeter of the circumscribed polygon VALUE OF 61,000000000000001,154700538379256,000000000000006,928203230275513,00000000000000<π<3,46410161513776 120,517638090205040,535898384862256,211657082460506,430780618346943,10582854123025<π<3,21539030917347 240,261052384440100,263304995174796,265257226562486,319319884195003,13262861328124<π<3,15965994209750 480,130806258460290,131086925630486,278700406093736,292172430262873,13935020304687<π<3,14608621513143 960,065438165643550,065473220825956,282063901781026,285429199290743,14103195089051<π<3,14271459964537 1920,032723463252970,032727844270626,282904944570926,283746099959653,14145247228546<π<3,14187304997982 3840,016362279207870,016362826807596,283115215823726,283325494113703,14155760791186<π<3,14166274705685 7680,008181208052470,008181276501576,283167784296646,283220353209383,14158389214832<π<3,14161017660469 1.5360,004090612582330,004090621138446,283180926456106,283194068643053,14159046322805<π<3,14159703432153 3.0720,002045307360680,002045308430196,283184211998546,283187497542703,14159210599927<π<3,14159374877135 6.1440,001022653814030,001022653947726,283185033384326,283185854770193,14159251669216<π<3,14159292738510 12.2880,000511326923720,000511326940446,283185238730776,283185444077233,14159261936538<π<3,14159272203861 24.5760,000255663463950,000255663466046,283185290067386,283185341404003,14159264503369<π<3,14159267070200 49.1520,000127831732240,000127831732506,283185302901546,283185315735693,14159265145077<π<3,14159265786784 98.3040,000063915866150,000063915866186,283185306110076,283185309318613,14159265305504<π<3,14159265465931 196.6080,00003195793308 6,283185306912216,283185307714343,14159265345610<π<3,14159265385717 HOW TO CALCULATE THE VALUE OF THROUGH THE PERIMETER OF THE INSCRIBED AND CIRCUMSCRIBED POLYGONS

12. Number of sides Value of DIFFERENT INTERVALS OF

13. Value of Number of sides Area of the inscribed polygon Area of the circumscribed polygon GRAPHIC OF THE APPROXIMATION OF