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Sunday, August 14, 2022

Aussie Maths researcher backs Baudhayana over Pythagoras

An Australian historian and researcher has applauded the Karnataka head of the NEP (National Education Policy) task force in India, Madan Gopal. Mr Gopal had recently suggested that it was Indian mathematician Baudhyana who had first put forward the theory now commonly referred to as the ‘Pythagoras’ theorem*.

While some say the matter of whether Baudhayana beat Pythagoras to the famous theorem is open to debate, Jonathan J. Crabtree, an advocate for Indian Maths said, “There’s no doubt NCERT* should refer to Baudhayana and not Pythagoras.”

Baudhyana is estimated to have lived around the 8th century BC in Bharat (Bharat being the Indigenous name of India) while Pythagoras is said to have lived in Greece around the 6th century BC.

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(Image Source: Jonathan Crabtree)

Furthermore, Mr Crabtree said, “It’s not enough to just change a name from Pythagoras to Baudhayana. What’s more important is India reclaims its long-lost title as Vishwa Guru or ‘World Teacher’. This can be done by expanding the standard compass and straightedge used in geometry to include rope or string as done long ago in Vedic times. The word Śulba in Śulbasūtras* literally means rope.”

“One example is the simple fact that planets orbit in an ellipse, unable to be drawn with a compass, yet easy with rope or string. Similarly, it’s impossible to square a circle with a compass and straightedge yet simple as revealed in my paper ‘Squaring a Circle with Rope’.”

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(Image Source: Jonathan Crabtree)

Mr Crabtree even has a video for children explaining how to square circles with rope. He has long been calling for Indic innovative change in Karnataka’s maths education. He recently gave a presentation for Virat Hindustan Sangam Karnataka on the topic Treasures of Post-Vedic Bharatiya Maths.  

Mr Crabtree’s story is a strange one. He became interested in Indian mathematics at the age of 7, in 1968. In Class 2 he noticed a loose thread. Zero was missing from his teacher’s explanation of multiplication.

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Over the years Mr Crabtree struggled to understand the maths he was being taught. Instead of intuitive common-sense explanations, he says he was given rules and laws to obediently obey.

In 1983 at age 21 he found himself in hospital with a shattered spine facing bleak news. If he moved; he might never walk again. So, he made a personal promise to fix maths if he was ever able to walk again.

Within a few years, he made headlines in Australia, when he said, “I hope to change the way the western world teaches maths.” Like a dog with a bone, Mr Crabtree never gave up on his promise. As if pulling a loose thread, he unravelled what he considers the feeble fabric of western math education to completely rebuild it from India’s zero.

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Hobsons Bay Leader (Image Source: Jonathan Crabtree)
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Geelong Advertiser (Image Source: Jonathan Crabtree)

Mr Crabtree says that perhaps the most extraordinary thing about Indian maths is it is so simple compared to the British maths curriculum schools follow around the world.

“The 18 maths sutras of Brahmagupta from 628 CE make everything fall into place. Importantly, his ideas are consistent with the basic laws of physics and the principle of symmetry.”

“For example, Brahmagupta defined zero as a sum of equal yet opposite numbers. Alas, today children are taught the absurd idea that 2 negatives are greater than 5 negatives in primary school, yet later told every action has an equal and opposite reaction in physics classes – consistent with Brahmagupta.”

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Mr Crabtree also mentions that his research reveals that India’s original zero-based maths was never fully understood in the Arabic world, so the version Europe received had been scrambled and was incomplete.” Children are taught 5 – 2 in Class 1 or 2 yet then wait five years to be taught 2 – 5.”

Yet, Mr Crabtree has devised a fun way for young children to learn these concepts. In his ‘Happy Harappan Brick and Hole Game’, a brick represents a positive and a hole represents a negative.

“Imagine a brick seller has two bricks for sale, yet a buyer wants five bricks. The solution is to add a zero, as per Brahmagupta’s Addition Sutra #5, positive plus zero is positive. The brick seller adds a zero by digging three holes to make three bricks. Now the seller has five bricks and three holes. The five bricks are then sold, and three holes remain. The maths model reveals why 2 – 5 =  –3.”

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Image Source: Jonathan Crabtree

Mr Crabtree has written to Bharta’s Education Minister Dharmendra Pradhan on several occasions regarding his in-depth research on Indian Maths. While he has not yet received a reply, he remains optimistic that either India or one of its neighbours will soon take his research into consideration.

For more information on Indian Maths visit www.podometic.in 

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Image Source: Jonathan Crabtree

Meanwhile, Mr Madan Gopal tweeted after The Australia Today published this article,

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*’Pythagoras’ theorem states that in a right-angled triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides.

*NCERT – The National Council of Educational Research and Training (NCERT) is an autonomous organisation set up in 1961 by the Government of India to assist and advise the Central and State Governments on policies and programmes for qualitative improvement in school education.

*Sulbasutras – Ancient Indian texts containing sections on Geometry. Well, known Mathematician David Henderson from Cornell University wrote about the Sulbasutras,

“As far as I have been able to determine these are the oldest geometry (or even mathematics) textbooks in existence. It is apparently the oldest applied geometry text.”

*Sutras – Aphorisms in ancient Indian texts

(The article was published on The Australia Today on July 22, 2022 and has been reproduced here.)

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