O tăbliță babiloniană de lut veche de 3.700 rescrie istoria matematicii – și ne arată că nu grecii au inventat şi dezvoltat trigonometria
Tableta este ruptă și probabil are lipsă mai multe rânduri, cred experții.
O tabletă de argilă de 3.700 de ani a dovedit că babilonienii au dezvoltat trigonometria cu 1.500 de ani înaintea grecilor și că au folosit o metodă sofisticată de matematică care ar putea schimba modul în care calculam astăzi funcțiile trigonometrice.
Tableta, cunoscută sub numele de Plimpton 332, a fost descoperită la începutul anilor 1900 în sudul Irakului de către arheologul american și diplomatul Edgar Banks, care a fost inspirația pentru Indiana Jones.
Adevăratul înțeles al tabletei a surprins până acum experți, dar cercetările efectuate de Universitatea din New South Wales, Australia, au arătat că este cea mai veche și cea mai exactă tabelă trigonometrică din lume, probabil folosită de arhitecții antici pentru a construi temple, palate și canale.
Cu toate acestea, spre deosebire de trigonometria de astăzi, matematica babiloniană a folosit baza de numerație 60, sau un sistem sexivimal, mai degrabă decât baza 10 care este folosit astăzi. Deoarece 60 este mult mai ușor de împărțit în trei, experții care studiază tableta, au constatat că calculele sunt mult mai precise.
„Cercetările noastre arată că Plimpton 322 descrie formele triunghiurilor cu unghi drept folosind un tip nou de trigonometrie bazat pe rapoarte, nu pe unghiuri și nu pe arcuri de cerc”, a declarat Dr. Daniel Mansfield de la Școala de Matematică și Statistică a Facultății de Științe a UNSW.
„Este o lucrare matematică fascinantă care demonstrează un geniu fără îndoială. Tableta conține nu numai cea mai veche tabelă trigonometrică din lume; Este, de asemenea, singurul tabel trigonometric complet precis, datorită abordării babiloniene foarte diferite a aritmeticii și a geometriei”.
„Aceasta înseamnă că are o mare relevanță pentru lumea noastră modernă. Probabil că matematica babiloniană a rămas fără aplicabilitate pentru mai mult de 3.000 de ani, dar ea are posibile aplicații practice în topografie, grafică pe calculator și educație”.
3,700-year-old Babylonian tablet rewrites the history of maths – and shows the Greeks did not develop trigonometry
The tablet is broken and probably had more rows, experts believe CREDIT: UNSW
A 3,700-year-old clay tablet has proven that the Babylonians developed trigonometry 1,500 years before the Greeks and were using a sophisticated method of mathematics which could change how we calculate today.
The tablet, known as Plimpton 332, was discovered in the early 1900s in Southern Iraq by the American archaeologist and diplomat Edgar Banks, who was the inspiration for Indiana Jones.
The true meaning of the tablet has eluded experts until now but new research by the University of New South Wales, Australia, has shown it is the world’s oldest and most accurate trigonometric table, which was probably used by ancient architects to construct temples, palaces and canals.
However unlike today’s trigonometry, Babylonian mathematics used a base 60, or sexagesimal system, rather than the 10 which is used today. Because 60 is far easier to divide by three, experts studying the tablet, found that the calculations are far more accurate.
“Our research reveals that Plimpton 322 describes the shapes of right-angle triangles using a novel kind of trigonometry based on ratios, not angles and circles,” said Dr Daniel Mansfield of the School of Mathematics and Statistics in the UNSW Faculty of Science.
“It is a fascinating mathematical work that demonstrates undoubted genius. The tablet not only contains the world’s oldest trigonometric table; it is also the only completely accurate trigonometric table, because of the very different Babylonian approach to arithmetic and geometry.
“This means it has great relevance for our modern world. Babylonian mathematics may have been out of fashion for more than 3000 years, but it has possible practical applications in surveying, computer graphics and education.
“This is a rare example of the ancient world teaching us something new.”
The Greek astronomer Hipparchus, who lived around 120BC, has long been regarded as the father of trigonometry, with his ‘table of chords’ on a circle considered the oldest trigonometric table.
A trigonometric table allows a user to determine two unknown ratios of a right-angled triangle using just one known ratio. But the tablet is far older than Hipparchus, demonstrating that the Babylonians were already well advanced in complex mathematics far earlier.
Babylon, which was in modern day Iraq, was once one of the most advanced cultures in the world
The tablet, which is thought to have come from the ancient Sumerian city of Larsa, has been dated to between 1822 and 1762 BC. It is now in the Rare Book and Manuscript Library at Columbia University in New York.
“Plimpton 322 predates Hipparchus by more than 1000 years,” says Dr Wildberger.
“It opens up new possibilities not just for modern mathematics research, but also for mathematics education. With Plimpton 322 we see a simpler, more accurate trigonometry that has clear advantages over our own.
“A treasure-trove of Babylonian tablets exists, but only a fraction of them have been studied yet. The mathematical world is only waking up to the fact that this ancient but very sophisticated mathematical culture has much to teach us.”
The 15 rows on the tablet describe a sequence of 15 right-angle triangles, which are steadily decreasing in inclination.
The left-hand edge of the tablet is broken but the researchers believe t there were originally six columns and that the tablet was meant to be completed with 38 rows.
“Plimpton 322 was a powerful tool that could have been used for surveying fields or making architectural calculations to build palaces, temples or step pyramids,” added Dr Mansfield.
The new study is published in Historia Mathematica, the official journal of the International Commission on the History of Mathematics.
