What is Pythagoras: Definition and 40 Discussions

Pythagoras of Samos (c. 570 – c. 495 BC) was an ancient Ionian Greek philosopher and the eponymous founder of Pythagoreanism. His political and religious teachings were well known in Magna Graecia and influenced the philosophies of Plato, Aristotle, and, through them, Western philosophy. Knowledge of his life is clouded by legend, but he appears to have been the son of Mnesarchus, a gem-engraver on the island of Samos. Modern scholars disagree regarding Pythagoras's education and influences, but they do agree that, around 530 BC, he travelled to Croton in southern Italy, where he founded a school in which initiates were sworn to secrecy and lived a communal, ascetic lifestyle. This lifestyle entailed a number of dietary prohibitions, traditionally said to have included vegetarianism, although modern scholars doubt that he ever advocated for complete vegetarianism.
The teaching most securely identified with Pythagoras is metempsychosis, or the "transmigration of souls", which holds that every soul is immortal and, upon death, enters into a new body. He may have also devised the doctrine of musica universalis, which holds that the planets move according to mathematical equations and thus resonate to produce an inaudible symphony of music. Scholars debate whether Pythagoras developed the numerological and musical teachings attributed to him, or if those teachings were developed by his later followers, particularly Philolaus of Croton. Following Croton's decisive victory over Sybaris in around 510 BC, Pythagoras's followers came into conflict with supporters of democracy and Pythagorean meeting houses were burned. Pythagoras may have been killed during this persecution, or escaped to Metapontum, where he eventually died.
In antiquity, Pythagoras was credited with many mathematical and scientific discoveries, including the Pythagorean theorem, Pythagorean tuning, the five regular solids, the Theory of Proportions, the sphericity of the Earth, and the identity of the morning and evening stars as the planet Venus. It was said that he was the first man to call himself a philosopher ("lover of wisdom") and that he was the first to divide the globe into five climatic zones. Classical historians debate whether Pythagoras made these discoveries, and many of the accomplishments credited to him likely originated earlier or were made by his colleagues or successors. Some accounts mention that the philosophy associated with Pythagoras was related to mathematics and that numbers were important, but it is debated to what extent, if at all, he actually contributed to mathematics or natural philosophy.
Pythagoras influenced Plato, whose dialogues, especially his Timaeus, exhibit Pythagorean teachings. Pythagorean ideas on mathematical perfection also impacted ancient Greek art. His teachings underwent a major revival in the first century BC among Middle Platonists, coinciding with the rise of Neopythagoreanism. Pythagoras continued to be regarded as a great philosopher throughout the Middle Ages and his philosophy had a major impact on scientists such as Nicolaus Copernicus, Johannes Kepler, and Isaac Newton. Pythagorean symbolism was used throughout early modern European esotericism, and his teachings as portrayed in Ovid's Metamorphoses influenced the modern vegetarian movement.

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  1. G

    Why did Pythagoras fear beans?

    Why did Pythagoras fear beans? Somebody told me two years ago it was for the same reason he bought only Ukrainian wheat from Whole Foods. Radiation poisoning. Two years since and I still haven't figured what he meant.
  2. R

    I have a real simple question about the Pythagoras theorem

    Here is the link. https://www.grc.nasa.gov/www/BGH/sincos.html Sorry just a little rusty on Pythagoras theorem. I mean the formula still holds but in order to find the opposite and the adjacent the opposite becomes the adjacent and vice versa .
  3. N

    Pythagoras 3D: Solve Problems with Ease

    I can do question a but not b nor c. Any help would be greatly appreciated
  4. akashpandey

    I Triangle law of vector addition and the Pythagoras theorem

    i know its pretty basic but please give some insight for triangle law of vector addition and pythgoras theorem. becuase ofcourse if you use traingle law to find resultant it will be different from what is pythagoras theorem
  5. S

    I Uncovering the 10 Classes of Ratios in Greek Mathematics

    In the book 'ZERO THE BIOGRAPHY OF A DANGEROUS IDEA' Charles Seife says, "Because ratios were the key to understanding nature, the Pythagoreans and later Greek Mathematicians spent much of their energy investigating their properties. Eventually, they categorized proportions into 10 different...
  6. mertcan

    I Generalisation of Pythagoras theorem

    hi everyone, I would like say that there are lots of proofs related to pythagoras theorem in a flat space, but When I searched it's general form I have not found something worthwhile. Besides, I also involved myself to have a nice proof of it, as a result I have not any valuable or very close...
  7. N

    Algebraic Proof for x in a Right Triangle: PS, SR, and RP on a Straight Line

    Homework Statement In a diagram, P, Q and R lie on a straight line and angle SQR is a right angle. The lengths PS, SR and RP are a, b and c cm respectively and QR is x cm. Use algebra to show that x = (b^2 + c^2 - a^2) / 2c Homework Equations and attempt at a solution[/B] Do I need to use...
  8. L

    How to find angle after applying Pythagorean Theorem?

    Hello, so I have a question that states (these aren't the actual measurements but they are around about the same, I can't remember the exact numbers so I made these up, this way I could apply the same to the actual numbers) an object being 4km above me, 1.4km to the north of me, and 2km to the...
  9. N

    Why does [sin(θ/2)-cos(θ/2)]^2 not always equal 1?

    Homework Statement Does [sin(θ/2)-cos(θ/2)]^2 equal 1 for all values of θ? I need to figure this out to solve a physics problem. Homework Equations sin^2(A)+cos^2(A)=1 The Attempt at a Solution [sin(θ/2)-cos(θ/2)]^2 =sin^2(θ/2)+cos^2(θ/2) =1 But this isn't what I get when I put...
  10. C

    Double Integral of Pythagoras over rectangular region

    Take any given point on the perimeter of a (A x B) rectange and then draw a line from that point to another point on one of the three remaining sides of the rectangle. What is the average length of the line? Well, the answer to that question involves integrals like this: \int_0^A \int_0^B...
  11. S

    Pythagoras Theorem: Is Variance of a Straight Line Zero?

    what makes Pythagoras theorm true? is it because variance of a straight line is zero?
  12. K

    Need help with pythagoras equations

    Hi, I need help with an explanation of how to deal with squareroots when solving equations. E.g. Look at the uploaded bmp.file and solve for x. Please I would like to have a full step by step method on how to deal with this type of equations in general. Thank you
  13. shounakbhatta

    Lorentz transformation and Pythagoras' theorem

    Hello, I was just going through some writings on the web reg.Lorentz transformation. Even considering the derivative factor,d, is anyway Lorentz transformation is some way, linked with Pythagoras' theorem? Correct me if I am wrong? -- Shounak
  14. Z

    Want to check the answer to this (Pythagoras)

    Homework Statement Find the coordinates of the points lying on the y-axis, P(0, y), when the distance between points P and A(5, 4) is 13. There is a diagram. Point B(0, 4) is also given. You can probably imagine how it looks like. Homework Equations The Attempt at a Solution...
  15. H

    Proveing Perpendicular of two vectors by applying Pythagoras rule

    Given that a=(a1,a2,a3) and b=(b1,b2,b3) by applying the Pythagoras rule, Prove that a1b1+a2b2+a3b3=0 if a and b perpendicular The Scalar product a.b = |a||b|CosQ -------------(1) if two vectors are perpendicular; Q=90degrees then CosQ=0; from (1) a.b=0 (a1,a2,a3).(b1,b2,b3)=0 a1b1+a2b2+a3b3=0...
  16. A

    Signature scheme by pythagoras theorem

    please help me :( i want to make signature scheme by pythagoras theorem
  17. J

    Complex numbers an Pythagoras' theorem.

    If c=\sqrt{a^{2}+b^{2}} would i be correct in saying c=|a+ib| ?
  18. K

    Will limit of discrete steps give Pythagoras theorem?

    Hi... It is an easy to see fact that, instead of moving along the hypotenuse of a right triangle, one starts from the lower corner and reach the upper corner moving only along the directions of the other two sides, i.e only vertically and horizontally and not diagonally...the distance moved...
  19. S

    Simplify Pythagoras Theorem Homework Statement

    Homework Statement I need to simplify vf = [(vcosx/2)^2+((2v-vsinx)/2)^2)]^1/2 as far as possible Homework Equations The Attempt at a Solution vf = [(vcosx/2)^2+((2v-vsinx)/2)^2)]^1/2 = [(v^2cos^2(x)+v^2sin^2(x)+4v^2+2vsinx)/2]^1/2 = [(v^2(1)+4v^2-2vsinx)/2]^1/2 ---- using...
  20. C

    Calculating the speed of a crane (using pythagoras) with different x & y speeds

    Hi, Homework Statement I'm designing a C++ program to simulate the operation of a steel processing warehouse. Part of my code requires me to calculate the time it takes for a crane to move certain distances (mainly diagonal ones) across a large shelving rack. Homework Equations The...
  21. T

    Finding the area using Pythagoras

    Homework Statement Hello; I am trying to solve what must be a ridiculously simple problem involving Pythagoras’ theorem and some simple geometry but I seem to be missing something. The problem is this: A farmer has a square field and has set up a drinking trough at a point in the middle...
  22. Z

    Euclid's Pythagoras Theorem proof

    Homework Statement Hi. I'm looking at Euclid's proof of the Pythagoras theorem. After cutting the square of the hypotenuse I don't understand why the area of the left rectangle (of the hypotenuse square) is equal to the area of the left square? Homework Equations The Attempt at...
  23. D

    Pythagoras and Vector coordinates of a cube.

    Homework Statement Basically we are given the coordinates for A=(13.0492, 30.9498, 9.01115) and C=(1.97687, 4.68868, 17.3632) which are two top corners of a cube that is sunk in the ground partway (specifically it's based on the cube near the Melbourne museum). But we don't know where the...
  24. E

    Pythagoras theorem - Shaft alignment TIR

    Homework Statement I am going the do some alignment of a shaft.I use a dial indicator for measurement, and use rim-face techniques. Then I need do calculate the total TIR (Total Indicated Runout). Here is my result of my measurement (Dial indicator). Top: 0 Right: +0,08 Bottom: -0,27...
  25. K

    Measuring distances: why the Pythagoras formula

    hi... We generally use the Pythagoras formula for distance between two points in 2D, when the Cartesian co-ordinates are given... One directly extends it to 3D..having the distance going as \sqrt{x^{2}+y^{2}+z^{2}}... For a curved co-ordinate system, we have distances measured by...
  26. X

    Pythagoras Theorem: Exploring Real vs Math Worlds

    Hi, I have a really stupid question :smile: suppose the base and perpendicular are both length 1 (whatever units) then the hypotenuse's length comes out to be SquareRoot of 2 but square root of 2 is 1.41421356.... (not a fixed number) so that means if i physically measure the...
  27. W

    Greeks vs Pythagoras: Universe Theory

    I understand the greek theory of the universe (Sphere's within sphere's within sphere's) but other than the fact the universe is based on mathematics, is there any other variations in the belief of the universe from the pythagoras?
  28. M

    Calculating the Distance between the Feet of a Stepladder: Sin Rule & Pythagoras

    Homework Statement The two sides of a stepladder are of length 2m and 1.85m. When fully opened, the longer side is inclined at 65° to the horizontal. Find the distance apart of the feet of the step ladder. Homework Equations Sin Rule & Pythagoras? The Attempt at a Solution I had a go but I...
  29. M

    The idea about Pythagoras stairs?

    Hello everybody I have looked everywhere for some good guides, so the question is: You probably know the Fibonacci sequence (1,1,2,3,5,8…) but there is a lesser-known sequence called (Pythagoras stairs) generated by a similar recursion formula. This is a sequence of pairs (Xn,Yn)...
  30. T

    How did Pythagoras come up with a^2+b^2=c^2?

    I have wondered about this for a while now and can anyone tell me the proof behind A^2+B^2=C^2?
  31. D

    Explaining Pythagoras' Theorem & Its Impact on Acceleration

    Can anyone explain to me why Pythagoras' Theorem governs the rate of change, of mass, length and time within accelertated bodies? It's a simple theorem learned by most children by the age of eleven, so one would expect the answer to this question to be quite simple as well.
  32. R

    Solving WWII Submarine Strike with Pythagoras and Differentiation

    [b]1. A WWII sub sailing north spots a Japanese carrier directly above it sailing due east at 10 knots. If the submarine at the time of sighting the carrier is 5 miles away, has torpedoes that travel 40 knots/hr, it takes 3 mins to load and fire torpedo. • At what angle with respect to...
  33. M

    Inner product Pythagoras theorem

    Hey guys, I am studying atm and looking at this book: "Introduction to Hilbert Space" by N.Young. For those who have the book, I am referring to pg 32, theorem 4.4. Theorem If x1,...,xn is an orthogonal system in an inner product space then, ||Sum(j=1 to n) xj ||^2 = Sum(j=1 to...
  34. R

    Pythagoras' Perfect Ratios: Uncovering the Base 10 Anomaly

    Base 10 Anomaly An applied 49-year study into the origin of pi and the Base 10 number system resulted in the finding of a highly anomalous formula. Essentially, the finding derives from the perfect ratios (0:1:1:2:3:4) given by Pythagoras who we know studied and perhaps taught in the...
  35. B

    Why is pythagoras theorem what it is?

    Why is the absolute distance sqrt(x^2 + y^2)? I've found several proofs on the internet but none really tell me much. I believe I have noticed something about pythagoras theorem and that is it allows all inertial reference frames in physics to be equivalent. In physics you can describe...
  36. E

    Applications of Derivatives using Pythagoras

    Hello. Could anyone help me with a few questions that I'm stuck on? Any suggestions would be much appreciatd. 1) A man 2m tall walks away from a lampost whose light is 5m above the ground. If he walks at a speed of 1.5 m/s, at what rate is his shadow growing when he is 10m from the lampost...
  37. A

    A dimensional proof of Pythagoras' thm

    I found this beauty and just had to post it here. It is on the second page of the following link: http://www.physics.smu.edu/%7Eolness/cteqpp/DimReg.5.pdf The rest of the file has to do with dimensional regularization, so you will need some more background to understand what is going on...
  38. marcus

    How much of Pythagoras was scientist, how much was mystic

    Pythagoras has a bad name for being a mystic he is known to have founded some kind of religious community in southern Italy where they reverenced the proportions of the universe or something (if you know more factual detail please fill in some) Also I have seen the opinion stated that he...
  39. P

    Pythagorean Theorem: Explaining A1=A2 & A4=A3

    http://www.ies.co.jp/math/java/geo/pitha1/pitha1-2.gif This is one of the many pythagorean proofs and I don't understand why A1=A2 and A4=A3? Can someone explain this to me please?
  40. H

    Pythagoras Theorem: 32 + 42 = 52?

    to work out a traingle side e.g. 52 is it we first times the 3 by itself to get 9 and then we times the 4 x 4 to get 16. then we take away the difference to get 52? 9 + 16 = 25 Formula 32 + 42 = 52 is this correct?