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How math professor Manjul Bharagava solved a 200-year-old number theory puzzle by using Sanskrit Texts & the Rubik’s Cube

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Manjul Bhargava

Manjul Bhargava

NEW YORK (Diya TV) — Manjul Bharagava, a mathematics professor at Princeton University and winner of the 2014 Fields Medal, has found the solution to a 200-year-old theory law with the help of a 6th Century mathematician and a Rubik’s Cube.

Bharagava said German mathematician Carl Friedrich Gauss showed that if two numbers — each sum of two perfect squares — are multiplied, the result will also be the sum of two perfect squares. The professor’s grandfather was a Sanskrit professor in Rajasthan, and said he’d once seen Sanskrit manuscripts written by Brahmagupta, an Indian mathematician from 628 CE, that carried a similar formula.

The similarity?

If two numbers are each the sum of a perfect square and a given whole number times a perfect square are multiplied together, the product will again be sum of a perfect square and that whole number times another perfect square.

When Bharagava came across the German’s 18th Century composition law on binary quadratic forms, he sought an easier way to simplify the process. The moment of truth came when Bharagava employed a Rubik’s and mini-cube, a more petite version with four squares on each side.

Bharagava discovered that if he placed numbers on each of the four corners of the mini-cube and cut it in half,  the eight corner numbers could be combined to produce a binary quadratic form. Even more, the cube had the capability to generate three binary quadratic forms when using this method since there were three ways to cut the cube in half.

The cube-slicing gave a new reformulation to Guass’ law.

Additionally, Bharagava found that if he arranged numbers on a Rubik’s domino, he could produce a composition law for cubic forms, ones whose exponents are three.

Ultimately, Bharagava discovered 12 more compositions, all which became part of his PhD thesis. Later, Benedict Gross, a mathematician from Harvard University, said the thesis was “first major contribution to Gauss’ theory of composition of binary forms for 200 years.”

 

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4 Indian Americans die, 2 missing in Hurricane Ida floods

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4 Indian Americans die, 2 missing in Hurricane Ida floods | Diya TV News

TRENTON (Diya TV) — At least four Indian Americans are dead and two missing as the massive floods ravaged New York and New Jersey following Hurricane Ida. Authorities say the victims were swept away by flood waters or drowned. Crews are using boats and drones, hoping to find more survivors.

https://youtu.be/0D7s6N2mNFo

In a historic moment, three women took oath as judges on India’s Supreme Court

Justices Hima Kohli, BV Nagarathna and Bela M Trivedi, were among the nine new appointees to the highest court of the land. Including these new appointments, the  Supreme Court has had 11 women judges in its history so far.

What a run for India at this year’s Paralympics. The athletes brought home 19 medals, including five gold. The medal count also included eight silver and six bronze.

Ravi Kapur contributed to this report.

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Modi to visit US in late September to meet Biden

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Modi to visit US in late September to meet Biden | Diya TV News

WASHINGTON DC (Diya TV) — Indian Prime Minister Narendra Modi will make his first U.S. visit since President Joe Biden took office. Modi is expected to travel to Washington DC and New York in the last week of September, according to top government officials. Modi and Biden have already met virtually on at least three occasions. Most recently at the G-7 summit this past June.

Congresswoman Pramila Jayapal of Washington is getting personal in her fight against the new Texas abortion law, which would ban terminating a pregnancy as early as 6 weeks.  The Indian American politician took to twitter to say getting an abortion years ago was not an easy choice, but it was her own choice. Jayapal says preserving this right is important for every woman across the US.

Mia Bonta is declaring victory in her California state Assembly race. She faced off against Indian American Democrat Janani Ramachandran in the District 18 special election.

Ravi Kapur contributed to this report.

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Census: Indian American population tops 4 million

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Census: Indian American population tops 4 million | Diya TV News

SPRINGFIELD, IL (Diya TV) — Illinois Congressman Raja Krishnamoorthi is touting the achievements of Indian Americans and their influence after the latest census data showing tremendous growth in the community. There are now more than four million Indian Americans and they’re considered one of the fastest growing ethnic groups.  Krishnamurthi says this is just the beginning and expects the community to contribute even more to the fabric of America.  

Pakistan National Security Adviser Moeed Yusuf is trying to walk back his controversial statements he allegedly made to a  British newspaper. The Sunday Times says he warned that the West risks a second 9/11 situation if it doesn’t “immediately recognize” the Taliban. The newspaper is standing by its reporting and says the entire interview was recorded.

A white man accused of running over a Sikh man outside a Colorado liquor store with his car is being charged with a hate crime.  Witnesses say Eric Breemen nearly killed Lakhwant Singh after a dispute. The Sikh Coalition advocacy group mobilized the community and helped push for the hate crime charges. 

Ravi Kapur contributed to this report.

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