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All you provided in terms of actual scriptural quotes are means by which geometrical constructions can be made. Such construction manuals with very very similar relations exist uiniversally and are found in Egypt, Sumer, Babylon and China. Without such manuals, nobody can make any big or small building whatsoever, and these were built everywhere, and methods for getting the geometry right are written about everywhere. The kind of algebraic proofs you included in the middle of the thread are completely anachronistic, the use of abstract symbols to represent the general principles of geometry apart from its use as a technology is far more recent and not found in any of these ancient texts from form any civilization.First you NEED to work upon your dates, your boot licking of western ideology and the dates borrowed from wiki are not helping you either.
Sulba Sutras provide numerical proof and so are the works of Āpastamba.
The Sulbasutras contain the geometry necessary for construction of the vedi and the agni for the obligatory and votive rites. These in turn are a part of the Kalpasutras , which are attached to the Vedas as one of the six V dangas or limbs of the Vedas. It is likely that the Sulbasutra sections were a part of the Srautasutras of the Yajur Veda, the Veda designed for the performance of sacrifices.
The three most primitive agni, Garhapatya, Aavaniya and Daksinagni, are older than the Rg Veda and the Mahavedi was likely known to the Indus Valley civilisation. The Sulbasutras deal with the correct construction of the vedi and agni including orientation, size, shape and areas and, as such, they are not meant as mathematical theorems or proofs. The geometry in the Sulbasutras can be categorised into that which expressly states theorems, constructions and implicit geometrical truths contained in constructions.
In the Yajur Veda and the Satapath Brahmana, 36 units is the length of the east-west line or praci or line of symmetry or prsthya of the Mahavedi and 30 units as one of the north-south lines. The praci and half the side make the sides containing the right angle in the triangle with sides 36, 15, and 39 units. There is a possibility that this theorem was known even earlier by the construction of the three agni, Garhapatya, Ahavaniya and Daksina. Other rational right triangles as well as the irrational right triangle 1,1 √2 and approximate right triangles are also mentioned in theSulbasutras (Amma 17-18).
There are several Vedic proofs for this theorem which are all fairly simple :
Proof I
The square AE = the square KG and the four congruent right-angled triangles all around it.
The areas are c2, (b-a)2 and 4( ½ ab) respectively.
So c2 = a2 – 2ab + b2 + 4( ½ ab) = a2 + b2
Proof I
Proof II
Construction:
CD = AB = m; DE = BC = n
So, ABC and CDE are congruent and ACE is a right-angled isosceles.
The trapezium ABDE = ABC + CDE + ACE
So ½ mn + ½ h2 + ½ mn = ½ (m + n) = ½ m2 + mn + ½ n2
So, ½ h2 = ½ m2 + ½ n2
So, h2 = m2 + n2
Proof II
Proof III
AE = BF = CG = DH = m and EB = FC = GD = HA = n
The square AC = the square EG + the four congruent right-angled triangles around it.
So, h2 + 4 (½ mn) = (m + n)2 = m2 + 2mn + n2
So, h2 = m2 + n2
Proof III
Proof IV
BD is perpendicular to AC.
So, triangles ABC, ABD and BCD are similar.
So, AB2/AC2 = ADB/ABC and BC2/AC2 = BCD/ABC
So, (AB2 + BC2)/AC2 = (ADB + BCD)/ABC = ABC/ABC = 1
So, AB2 + BC2 = AC2
Proof IV
Proof V
Using coordinates, the distance between point A at (a,0) and point B at (0,b) is:
BA = √ [(a – 0)2 + (0 – b)2] = √ (a2 + b2).
Following are a selection of constructions given in the Sulbasutras (Amma 23-46).
i) Drawing two perpendicular diameters in a circle in Baudhayana’s recipe for drawing a square.
Drawing a line one fixes a pin at its middle. Slipping the end ties on to this pin, one draws a circle with the mark (the middle of the cord) and fixes pins at the ends of the diameter. With the end-tie on the eastern pin one draws a circle with the whole cord. Similarly at the western pin. The second diameter should be stretched through the points where these (circles) intersect.
This method is well known in later Indian mathematics as the ‘fish’ method due to its shape.
'Fish' Method
ii) The construction of a square with a given side results in a beautiful geometrical pattern.
Wishing to construct a square one should make ties at both ends of a string as long as the desired side and make a mark at its middle. One should draw a line and fix a pin at its middle. Fixing the ties on this pin one should draw a circle by the middle mark (of the cord) and at the ends of the diameter (formed by the praci) one should fix pins. Fixing one tie on the eastern pin one should draw a circle with the other tie. Similarly round the western pin. Through the points where they meet the second diameter should be drawn and pins should be fixed at this end. With the ties on the eastern pin a circle is to be drawn with the middle mark. Similarly round the southern, western and northern (pins). Their outer points of intersection form the square.
This method is found in the Baudhayana Sulbasutra.
Transformation of Figures
Different shapes were prescribed for the fire-altars depending on the benefit sought: the falcon or syenacit for attaining heaven, the isosceles triangle or praugacit for destroying enemies etc. However, the shapes had to have the same area of 7 ½ square purusas and therefore the Sulbasutras described different methods of changing the shapes of figures while retaining the same areas.
To convert a square into a circle
The Sulbasutras give an approximate construction, which results in a value of π of 3.088. Whether or not it was known at the time that this method indeed results in an approximation is not known.
If a is the side of the square and r the radius of the circle then r = a(2 + Ö2)/6.
If a = 1, then the area of the square is 1, r = (2 + Ö2)/6 = 0.5690355 and the area of the circle (using today’s value of π) is 1.0178256.
Convert a Square to a Circle
To convert a square into a rectangle
One method is given by:
Wishing to transform a square into a rectangle one should cut diagonally in the middle, divide one part again and place the two halves to the north and east of the other part. If the figure is a quadrilateral one should place together as it fits. This is the distribution.
Convert a Square to a Rectangle
And remember, this coming from a small portion of this one Sulbha shastra and your post is ****e
Basically you are admitting the works to India, and you do NOT understand what numerical proofs are , and your post does not make sense where you claim these existed in egypt , china and other, can you post proof of these existing works in china ?All you provided in terms of actual scriptural quotes are means by which geometrical constructions can be made. Such construction manuals with very very similar relations exist uiniversally and are found in Egypt, Sumer, Babylon and China. Without such manuals, nobody can make any big or small building whatsoever, and these were built everywhere, and methods for getting the geometry right are written about everywhere. The kind of algebraic proofs you included in the middle of the thread are completely anachronistic, the use of abstract symbols to represent the general principles of geometry apart from its use as a technology is far more recent and not found in any of these ancient texts from form any civilization.
History follows its own methods and date texts according to the balance of evidence, not faith.
A claim made with no evidence I believe.Also can @sayak83 post us who were the first discoverers of
1. Fibonacci Series
2. Binomial numbers
3. Binary numbers
4. Pascal Triangle
5. Calculus
6. Trigonometry
Clue: All of these originated from bhArat,
what ? Can you answer the question or just backing away from answering ? I am asking you a question not answering, I would later answer that after you reply with answers. If you cannot answer, admit that you lost the argumentA claim made with no evidence I believe.
Egypt and babylon certainly had their own advanced math. Entire books.Basically you are admitting the works to India, and you do NOT understand what numerical proofs are , and your post does not make sense where you claim these existed in egypt , china and other, can you post proof of these existing works in china ?
Also, I am waiting for your reply on my earlier post
Nobody can claim to have invented any of the the first 4 and trigonometry as every civilization has ancient texts that refer to results pertaining to them. Calculus was invented by Leibniz and Newton, though the concept of infinitesimals was used previously.what ? Can you answer the question or just backing away from answering ? I am asking you a question not answering, I would later answer that after you reply with answers. If you cannot answer, admit that you lost the argument
what does it mean ?Nobody can claim to have invented any of the the first 4
http://www.cbc.ca/news/technology/calculus-created-in-india-250-years-before-newton-study-1.632433Calculus was invented by Leibniz and Newton,
Just in case there is any confusion. Algebra and the decimal number system was definitely invented as a specialized mathematical discipline in India, but not in Vedic time.Nobody can claim to have invented any of the the first 4 and trigonometry as every civilization has ancient texts that refer to results pertaining to them. Calculus was invented by Leibniz and Newton, though the concept of infinitesimals was used previously.
we could reserve this discussion for another time because we are not discussing about decimal sys now, but let me know what exactly did you mean when you saidJust in case there is any confusion. Algebra and the decimal number system was definitely invented as a specialized mathematical discipline in India, but not in Vedic time.
LOL. "Calculus" was "invented" by Archimedes in 3rd century BC when he explicitly calculated the area of a parabola by the quadrature formula of using smaller and smaller triangles.http://www.cbc.ca/news/technology/calculus-created-in-india-250-years-before-newton-study-1.632433
https://en.wikipedia.org/wiki/Kerala_school_of_astronomy_and_mathematics
Calculus was created and used in India 250 years before newton was born, so there you go!
You are DEFEATED in Q#5 , calculus part
I would later respond on these queries, I am eagerly waiting for the answers to the first 4 pointsLOL. "Calculus" was "invented" by Archimedes in 3rd century BC when he explicitly calculated the area of a parabola by the quadrature formula of using smaller and smaller triangles.
http://web.calstatela.edu/faculty/hmendel/Ancient Mathematics/Archimedes/QuadraturaParabolae/QP.contents.html
Your absurd idea that somehow the contributions required in making calculus possible when it comes from India counts as "invention" while all other contributions coming from all other places do not count as such is illogical, bigoted and narrow.
Archimedes did NOT invent calculus,LOL. "Calculus" was "invented" by Archimedes in 3rd century BC when he explicitly calculated the area of a parabola by the quadrature formula of using smaller and smaller triangles.
http://web.calstatela.edu/faculty/hmendel/Ancient Mathematics/Archimedes/QuadraturaParabolae/QP.contents.html
Your absurd idea that somehow the contributions required in making calculus possible when it comes from India counts as "invention" while all other contributions coming from all other places do not count as such is illogical, bigoted and narrow.
I have already replied. Nobody invented them. individual mathematical relations crop up so often in so many places that its silly to name an inventor. Calculus was invented in Europe as a specialized mathematical discipline (using contributions from everywhere certainly) and trigonometry existed as a specialized discipline since the dawn of civilizations.@sayak
I would later respond on these queries, I am eagerly waiting for the answers to the first 4 points
Actually he is specifying the speed of light. Your objection is common, but his commentary says specifically "tatha ca smaryate" or "it is remembered here" and since the Rg Veda verse in question is specifically glorifying the light aspect of the sun (it brightens the sky, and travels very fast), it is reasonable assumption to make that Sayana is speaking about light here.
I would disagree with that statement. Many ideas and knowledge that the Greeks first had came from India (when Alexander the Great established trade routes between the two countries ).
I am afraid the Vedas claim that from the start. The Aitareya Brahmana (3.44) declares:
"The Sun does never set nor rise. When people think the Sun is setting it is not so. For after having arrived at the end of the day it makes itself produce two opposite effects, making night to what is below and day to what is on the other side. Having reached the end of the night, it makes itself produce two opposite effects, making day to what is below and night to what is on the other side. In fact, the Sun never sets."
No this does not specifically say the earth is spherical,
I think I did see the verse in Rg Veda that mentioned "Bhugolam".
Can you quote a verse from any of the four Vedas to backup this statement? A single verse will do.
For lack of evidence, obviously. It is better to accept an incomplete story grounded in facts than a complete story which has no corroboration. Besides, the Christians and Muslims claim their religious theory of origins are complete as well. So there is nothing unique about this claim about completeness
No. Rather, we have people here who have no clue about the Veda and are imagining it be some kind of encyclopedia - which it most certainly is not. The proof for this is the simple fact that long posts about the glory of the Veda are not backed by a single reference.
No, he is not. Go educate yourself about Agnivesha and Hippocrates.
Namaskaram.
l will do without the implication that I must be either deffective or ashamed of being an atheist, if you do not mind. Or even if you do, really.
It ill fits me, you know. Nor can I in good faith refuse my perceived duty to challenge theistic assumptions when they threaten to disturb the learning of truth and proper religions practice.
I take it that you mean here that the scientific theory of evolution is an example or stance of a more abstract or cosmic principle that you are also calling Evolution. But I am not certain, since you began this post by saying that they are at odds with each other. Or maybe you just want to underscore that you think we should consider Buddhist Cosmology as so much more ambitious and realized than the biological theory? I honestly don't know.
Science is not sentient, while people are. If there is a duty, it must be acceptd by the people, not the abstract discipline. Not sure why you feel we have such specific duties, though.namaskaram sayaK ji
if one is interestes in Mathematics then we must return to the Vedic cosmology it will confirm much that we are strugling to comprehend , ..further more it will give it in the context of Sentient existance , if Science is not aiming at universal understanding then the perfection of one science alone will bring dissharmony and imballance to life , ....
It is a deliberately self-limiting approach that, while perhaps not as fulfilling to people who look for awe and inspiration over reliability of certainties, nonetheless makes a whole lot of sense and protects us all from dangerous assumptions and serious mistakes.
Not sure what you mean here. At first glance it feels like some sort of appeal to keep true to awe for awe's sake. I really don't know.
A Dharmi should not feel any unease at doing his or her best to skillfully understand and deal with the world as it manifests towards us all. Fear of learning better is not a virtue by any means.
This, I suppose must be considered a situation of misassignment of blame, or perhaps of simple abuse of the purpose and scope of religious texts. There is little else to conclude from this paragraph.
I have to wonder how you came to these concepts of "true" and "secular" sciences, as well as what you mean by "rejection" of the Vedas.