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.


Dr Daniel Mansfield with the 3,700-year-old trigonometric table Credit: UNSW

“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.

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Jadi sebenarnya matematika, bukan berasal dari yunani, tapi dari Babylonia

Sudah mulai banyak fakta yg dibongkar arkeolog tentang Babylonia yg tidak sesuai dengan isi kitab suci.......

Di perjanjian lama, dikatakan kalau menara Babylon dihancurkan oleh Tuhan, karena menara dibangun manusia untuk mencapai langit, alias untuk menandingi Tuhan

Namun berdasarkan penelitian arkeologi yg terbaru, terbuka fakta yang sebenarnya jikalau menara babylon musnah karena perbuatan manusia, bukan akibat kemurkaan Tuhan

Alkisah Nimrod merancang pembangunan menara untuk studi astrologi nya, namun pembangunan menara terhenti karena ulah salah satu bani Israel yg doyan bentuk ormas okp, dimana suka memalak proyek menara dengan berbagai cara :

1. Uang kerohiman pribumi mesopotamia

2. Uang keamanan ormas pemuda Babylonia (kolaborasi dengan mafia asal Mohenjo-Daro)

3. Uang iuran serikat budak penarik batu besar

4. Uang jaminan Cambuk berlogo SNM (Standard Nasional Mesopotamia)

5. Uang harian pemuda Sumeria setempat

6. Uang parkir berdasarkan waktu posisi matahari dan bulan, seperti parkir keledai, parkir gerobak kayu, parkir kereta pedati pengangkut batu gede (parkir kelas satu) dan parkir kaki, parkir berteduh, parkir pejalan kaki lamban (parkir kelas dua)

7. Uang izin bongkar muat batu besar (izin saja)

8. Uang izin mengangkut batu besar dari pedati ke menara (sekali lagi izin saja)

9. Uang makan bersama pemuda Hitties

10. Uang izin kuli panggul untuk batu ukuran kecil hingga menengah

11. Uang izin mencambuk utk para mandor menara babylonia

12. Uang suka suka sewaktu waktu, sekitar 50-100 sheqel sekali palak (sehari bisa 3-5 kali)

13. Uang kerohiman pemuda Assyria

14. Uang muda mudi Mandaean

15. Uang Sumbangan paksa Ikatan Pemuda Akkadian

16. Uang Laskar Berak Kali Sei Euphrates

17. Uang Izin Mendirikan Bangunan dari komunitas Bang Gilgamesh (lagi bersaing dengan Uruk Gubaru memperebutkan posisi gubernur Babylonia, jadi butuh sheqel banyak)

18. Uang Keamanan Material Proyek Menara Dari Forum Putra Putri Pasukan Babylonia

19. Uang Jaminan Kelancaran Proyek Menara dari Pemuda Merga Syria

20. uang sertifikasi Serikat budak pekerja pembangunan Ziggurat

21. uang tanah adat Himpunan Kasim (budak yg dikebiri)

22. uang pembebasan lahan proyek utk suku nomad amorites (modal dengkul dudukin lahan orang)

23. dst..............

Pola pemakaian berbagai nama bani lain dan etnis lain untuk memeras, tapi manusia nya itu2 juga alias dari bani yg sama, menimbulkan adu domba dan kemarahan bani2 Israel yang lain, akhirnya terjadi perang saudara, kerajaan babylonia pecah dan menara babylon pun musnah....

Pasca perang, para bani2 Israel musyawarah mufakat untuk menganggap bani pemalak ini sebagai bani aib, menendang mereka dari asia tengah (sekarang namanya timur tengah) dan menghapus bani aib ini dari catatan sejarah Israel, dengan mengatakan "menara Babylon musnah karena kemurkaan Tuhan" (ada 2 versi, yang satu Tuhan marah karena manusia mencoba menandingi Tuhan, dan versi lain mengatakan kalau Tuhan marah karena ingin bangsa Israel untuk menyebar bukan berpusat di menara)

Beberapa perkamen kuno menunjukkan indikasi kalau bani aib ini eksodus ke polynesia (kepulauan) di kawasan tenggara asia, dan kabar nya sekali lagi bani aib ini sukses menjadi aib untuk kerajaan di kawasan asia tenggara.........

Ane kabur dulu ke afghan sebelum di boenoeh dan di makan hidup2 oleh bani yg satu ini