1. Using rope to square a circle
2. Aryan invasion theory is a complete myth
3. Ashoka was a Buddhist when he invaded Kalinga
4. Pythagoras Theorem was known centuries before - Baudhayana Śulbasûtra.
5. Using rope to divide circle into any number of parts (including prime #s)
6. Hitler's cross is hooked cross, Hakencruz, not Swastika
7. Fibonacci sequence from poetry and meter
1. Using rope to square a circle
What is squaring a circle?
It is drawing a square equal to the area of a given circle.
Area of a circle = Pi*r^2 where r is the radius of the circle
Area of square = s^2 where s is the side of the square
Therefore Pi*r^2=s^2
implies s= r*sqrt(Pi)
But Pi is a transcadental number. Therefore its square root cannot be computed exactly
This squaring of a circle using a compass and straight edge is considered impossible.
Hence squaring a circle is used by many as a metaphor for doing the impossible.
However it can be easily done via a rope as explained the Sulbasutras.
The Sulbasutras are appendices to the Vedas which give rules for constructing altars.
(Sanskrit śulba: "string, cord, rope") are sutra texts belonging to the Śrauta ritual. Śrauta is a Sanskrit word that means "belonging to śruti", that is, anything based on the Vedas of Hinduism. It is an adjective and prefix for texts, ceremonies or person associated with śruti.
In Bharat 800 BCE when the Śulba Sūtras (rules of rope) were written ropes were used for altar construction.
As per method surfaced again by Maths historian Jonathan Crabtree (@jcabtree on twitter. podometic.in his website on ancient Bharatiya mathematics) (See eminent Prof. C. K. Raju's work as well)
Method:
1. Take a circle with radius = 1 unit (say 1 inch).
Circumference of circle = 2*pi*r= 2*pi in this case.
Area = pi*r*r = pi in this case
2. Use a rope and measure 1/4th of the circumference of the circle. Make this length = a
a= (1/4)*2*pi = pi/2
3. Now put that same rope along the vertical diameter of the circle.
4. From the point where the rope finishes on the vertical diamater of the circle, draw a line parallel to the horizontal diameter of the circle to intersect the circle. Now join the top part of the rope to this point of intersection to form the hypotenuse of the triangle. This side is the side of your square.
Length of side = sqrt(pi). (Proof given below). Area of square using that (c) as side = sqrt(pi)*sqrt(pi) = pi = Area of circle.
The proof given by Jonathan Crabtree is a bit lengthy and complicated.
So here is a considerably easier proof using Pythagoras/Baudhayana theorem:
Remember radius of the circle is 1 unit (1 inch)
https://www.intmath.com/plane-analytic-geometry/squaring-the-circle.php
2.
Aryan invasion/migration theory - a complete myth:The theory of the Aryan invasion (or migration) was first put forward by Western scholars during the colonial age. It maintained that a race of European or Central Asian “Aryans” swept into the subcontinent displacing the indigenous Indus Valley Civilisation. Theory states it was the "Aryans" who brought in Vedas and many other aspects into Indian culture.
This is what we have learnt in our schools.Its a complete myth and distortion of facts . The AIT or AMT has been completely debunked. I will refer to it as AIT unless required to specify otherwise.
It was used/still being used to:
1. Further colonial superiority of the people from Europe/central Asia
2. Divide Indian people into northern "Aryans" and southern "Dravidians"
There is no such thing as "Aryans". The word Arya was used to mean noble person.
The AIT has been debunked on multiple fronts:
1. Archeological findings: 2. Textual findings 3. Genetic findings 4. Linguistic findings
"How can ‘they’ say South Indians are different from North Indians- the genetic heritage is same- R1a & ‘R’ancestral lines are found among many Indians regardless of caste, tribe or region. Who wants to fuel this Aryan & Dravidian divide?"
"India is the first continent founded after Africa. India has the oldest female & male genetic lines. Continuous occupation since 80KYA. Agriculture originated 12KYA separately in India. No migrations/population replacement. India is India & Indians are Indians. #NoAryans"
For couple of other examples on how AIT has been debunked:
1. Archeological example : Along the bank of the Sarasvati (now called the Ghaggar) is located Kalibangan, a site of the Harappan Civilization. It had to be abandoned while it was still in a mature stage, owing to the drying up of the adjacent river. According to the radiocarbon dates, this abandonment took place around 2000. Since, as already stated, during the Rigvedic times the Sarasvati was a mighty flowing river and it dried up around 2,000 BCE, the Rigveda has got to be earlier than 2000 BCE. How much earlier is anybody’s guess; but at least a 3rd millennium BCE horizon is indicated.
2. Textual findings: Comparision of the timelines of the New&old Books (Mandalas) of RigVeda with the well known&dated "Indo-Aryan" Mittanis and with that of Avestan Iranians literature (The Avesta) shows the new RigVeda books dated at atleast a couple of centuries before 2000 BC and the older RigVeda books atleast some centuries before that.
3. Ashoka was a Buddhist when he attacked Kalinga and Ashoka the not so great:
"Ashoka waged Kalinga war in the 8th year of his reign.
Direct evidence from Simhalese historical chronicle "Mahavamsa' clearly mentions that Ashoka became a Buddhist in the 4th year of his reign proving beyond a doubt that he was a Buddhist when he waged Kalinga war.
Sources:
1) The Mahavamsa
2) The rock edits of Ashoka
3) Divyavadana"
"According to the official narrative, Ashoka was horrified by his own brutality and became a Buddhist and a pacifist. However, as we have seen, he was already a practicing Buddhist when he invaded Kalinga. Moreover, from what we know of his early rule, he was hardly a man to be easily shocked by the sight of blood. The main evidence of his repentance comes from his own inscriptions. However, it is very curious that this “regret” is mentioned only in locations far away from Odisha (such as in Shahbazgarhi in north-western Pakistan). None of the inscriptions in Odisha express any remorse; any hint of regret is deliberately left out.
Surely, if Ashoka was genuinely remorseful, he would have bothered to apologize to the people whom he had wronged. Far from it, he does not even offer to free the captives. Even the inscriptions where he expresses regret include a clear threat of violence against other groups like the forest tribes who are unequivocally “told of the power to punish them that Devanampriya possesses in spite of his repentance, in order that they may be ashamed of their crimes and may not be killed”[2]. This is no pacifist.
It appears that Ashoka was using his inscriptions as a tool of political propaganda to counter his reputation for cruelty."
" The Pali text Ashoka-vadana, moreover, tells us of more acts of genocide perpetrated by the emperor many years after he supposedly turned pacifist [3]. These were directed particularly at followers of the Jain and Ajivika sects; by all accounts he avoided conflicts with mainstream Hindus and was respectful towards Brahmins. The Ashokavadana clearly tells us how an enraged Ashoka had 18,000 Ajivikas in Bengal put to death in a single episode."
Now question comes, why has Ashoka been built up ?
1. "This standard narrative is found in school textbooks and most Marxist histories of India. It is intended to neatly contrast Bad Hinduism versus Good Buddhism." - TrueIndology
2. From Sanjeev Sanyal's article : "As one can see, Ashoka does not look like such a great king on closer inspection but as a cruel and unpopular usurper who presided over the disintegration of a large and well-functioning empire. This fits with the fact that he is not remembered as a great monarch in the Indian tradition but in hagiographic Buddhist texts written in countries that did not experience his reign. He was “rediscovered” in the 19th century by colonial era orientalists like James Princep. His elevation to being “Ashoka the Great” is an even more recent and is the result of political developments of the first half of the twentieth century."
"Some leaders of the freedom movement such as Jawarharlal Nehru decided to create a lineage for their socialist leanings.Emerging class of socialist Indian politicians stumbled upon Ashoka’s inscriptions. Ashoka clearly speaks of government intervention in the day-to-day lives of his subjects."
4. Pythagoras Theorem was known centuries before - Baudhayana theorem. Expressed in in Baudhayana Śulbasûtra. Also Pythagorean triplets were used by Babylonians well before Pythagoras
Pythagoras lived in the time period of about 570-490 BCE.
Baudhayana is dated to be around 800 BCE.
The actual shloka (verse) in Baudhāyana Śulbasûtra that describes Pythagoras theorem is given below :
दीर्घचतुरश्रस्याक्ष्णया रज्जु: पार्श्र्वमानी तिर्यग् मानी च यत् पृथग् भूते कुरूतस्तदुभयं करोति ॥
dīrghachatursrasyākṣaṇayā rajjuḥ pārśvamānī, tiryagmānī,
cha yatpṛthagbhūte kurutastadubhayāṅ karoti.
A rope stretched along the length of the diagonal produces an area which the vertical and horizontal sides make together.[7]
Baudhāyana also presented geometrical proof using isosceles triangles so, to be more accurate, we attribute the geometrical proof to Baudhāyana and numerical (using number theory and area computation) proof to Āpastamba. Also, another ancient Indian mathematician called Bhaskara later provided a unique geometrical proof as well as numerical which is known for the fact that it’s truly generalized and works for all sorts of triangles and is not incongruent (not just isosceles as in some older proofs).
A Babylonian tablet, Plimpton 322 has the world's oldest trigonomtric table (known so far) and has special pattern of numbers called Pythagorean triplets. It is believed the tablet was created in the ancient Sumerian city of Larsa sometime between 1822 and 1762 BC.
Of course this doesn't necessarily prove they presented it in the form of a theorem or proved it. But its clear knew the use of Pythagorean triplets for practical purposes.
5. Using rope to divide circle into any number of parts (including prime #s)
From mathematician Jonathan Crabtree (podometic.in)
"The division of a circumference into any integral number of petals is trivial when you use rope as per the 800 BCE Śulbasūtras"
"I hope this diagram helps explain how to draw any number of petals around a circle regardless of whether they are prime or not.
Remember, the Greeks banned India's use of rope, saying only a straight edge and compass could be used, so many solutions in geometry were NOT found!"
Application to a real life problem:
Lotus found at #Janmabhoomi poses a challange to modern Maths & Engineering. Outer whorl has 29 equal petals & inner has 13; both 'prime' numbers & 360°circle not divisible by 13 or 29.
Division into prime # of parts done using the rope method mentioned above. Draw the sectors of the circle (prime # of them) and then create the petals inside.
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