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> Brahmagupta was the first to have a formula for area of cyclic quadrilateral in 6th century That's not analytic geometry. > Bhaskara had devised ideas of di

> Brahmagupta was the first to have a formula for area of cyclic quadrilateral in 6th century That's not analytic geometry. > Bhaskara had devised ideas of differential calculus by 11th century [2]. A concrete example of this is the use of sine and cosine series in Kerala School of Mathematics [3]. I don't think these count as analytic geometry. Analytic geometry has a specific meaning: https://en.wikipedia.org/wiki/Analytic_geometry https://en.wikipedia.org/wiki/Analytic_geometry

jimsimmons 5y ago
Yeah read the distance and angle section. Describing geometric objects with equations in coordinate system is analytic geometry. Anyway I’m not going to seriously discuss with you because it’s clear from your post history that your replies are avalanches of pedantry. If you think it has a specific meaning, elaborate it and identify the point of divergence or express what your view is. I don’t have an obligation to convince you.
- alentist 5y ago
  > read the distance and angle section. Distances and angles have been used by the Greeks since ancient times. By themselves they don't constitute analytic geometry. > Describing geometric objects with equations in coordinate system is analytic geometry. Yes, and the example you gave does not satisfy that definition.
  - jimsimmons 5y ago
    Have you studied math? I know Greeks used angles and distances lol. The point is how. Did they describe them algebraically or did they do the Euclidean thing where they “take a compass and bisect and you’ll see each part is equal to this other side”. Euclid/Greeks used pure geometry. They might have had all geometric concepts. But they didn’t manipulate algebraic equations to obtain geometric insights. And yes that is analytic geometry
    - alentist 5y ago
      > Have you studied math? Yes, I have a degree in it. > And yes that is analytic geometry No, the example you gave is not analytic geometry. Read the definition again. The explicit use of a coordinate system is essential. Algebra is not sufficient.
      - jimsimmons 5y ago
        From the wiki of synthetic geometry [1]: > Synthetic geometry (sometimes referred to as axiomatic geometry or even pure geometry) is the study of geometry without the use of coordinates *or formulae*. It relies on the axiomatic method and the tools directly related to them, that is, compass and straightedge, to draw conclusions and solve problems. > Only after the introduction of coordinate methods was there a reason to introduce the term "synthetic geometry" to distinguish this approach to geometry from other approaches. From wiki of analytic geometry [2]: > In classical mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This *contrasts* with synthetic geometry. I know you’re using this to dismiss my case but the first line of Wikipedia hardly a standard for definition. Further down in the same article: > *Usually* the Cartesian coordinate system is applied to manipulate equations for planes, straight lines, and squares, often in two and sometimes three dimensions. > As taught in school books, analytic geometry can be explained more simply: it is concerned with defining and representing geometrical shapes in a numerical way and extracting numerical information from shapes' numerical definitions and representations. Putting it together: 1. The classic western geometry was predominantly non-synthetic, with the term “synthetic” being introduced much later in order to differentiate pure geometry from Analytic/algebraic forms 2. Use of formulae is outside the scope of pure geometry ala Euclidian style. 3. Distances and angles are geometric shapes. Trigonometry using algebra is part of analytic geometry. 4. Indian mathematicians used formulae and algebraic manipulations to arrive at geometric insights, including developing trigonometric identities and series. 5. Explicit use of coordinate system is not essential. It’s “usually” used. 6. Descartes didn’t invent the number line. He only proposed a coordinate system. Number line itself was a much later development. Descartes’ coordinates were a lot more abstract. If using the modern coordinate system is your criteria for analytic geometry, when was it finally established? What am I missing? Genuinely curious and happy to be completely wrong here. [1] https://en.wikipedia.org/wiki/Synthetic_geometry https://en.wikipedia.org/wiki/Synthetic_geometry [2] https://en.wikipedia.org/wiki/Analytic_geometry https://en.wikipedia.org/wiki/Analytic_geometry

jimsimmons 5y ago

Yeah read the distance and angle section. Describing geometric objects with equations in coordinate system is analytic geometry. Anyway I’m not going to seriously discuss with you because it’s clear from your post history that your replies are avalanches of pedantry. If you think it has a specific meaning, elaborate it and identify the point of divergence or express what your view is. I don’t have an obligation to convince you.

alentist 5y ago
> read the distance and angle section. Distances and angles have been used by the Greeks since ancient times. By themselves they don't constitute analytic geometry. > Describing geometric objects with equations in coordinate system is analytic geometry. Yes, and the example you gave does not satisfy that definition.
- jimsimmons 5y ago
  Have you studied math? I know Greeks used angles and distances lol. The point is how. Did they describe them algebraically or did they do the Euclidean thing where they “take a compass and bisect and you’ll see each part is equal to this other side”. Euclid/Greeks used pure geometry. They might have had all geometric concepts. But they didn’t manipulate algebraic equations to obtain geometric insights. And yes that is analytic geometry
  - alentist 5y ago
    > Have you studied math? Yes, I have a degree in it. > And yes that is analytic geometry No, the example you gave is not analytic geometry. Read the definition again. The explicit use of a coordinate system is essential. Algebra is not sufficient.
    - jimsimmons 5y ago
      From the wiki of synthetic geometry [1]: > Synthetic geometry (sometimes referred to as axiomatic geometry or even pure geometry) is the study of geometry without the use of coordinates *or formulae*. It relies on the axiomatic method and the tools directly related to them, that is, compass and straightedge, to draw conclusions and solve problems. > Only after the introduction of coordinate methods was there a reason to introduce the term "synthetic geometry" to distinguish this approach to geometry from other approaches. From wiki of analytic geometry [2]: > In classical mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This *contrasts* with synthetic geometry. I know you’re using this to dismiss my case but the first line of Wikipedia hardly a standard for definition. Further down in the same article: > *Usually* the Cartesian coordinate system is applied to manipulate equations for planes, straight lines, and squares, often in two and sometimes three dimensions. > As taught in school books, analytic geometry can be explained more simply: it is concerned with defining and representing geometrical shapes in a numerical way and extracting numerical information from shapes' numerical definitions and representations. Putting it together: 1. The classic western geometry was predominantly non-synthetic, with the term “synthetic” being introduced much later in order to differentiate pure geometry from Analytic/algebraic forms 2. Use of formulae is outside the scope of pure geometry ala Euclidian style. 3. Distances and angles are geometric shapes. Trigonometry using algebra is part of analytic geometry. 4. Indian mathematicians used formulae and algebraic manipulations to arrive at geometric insights, including developing trigonometric identities and series. 5. Explicit use of coordinate system is not essential. It’s “usually” used. 6. Descartes didn’t invent the number line. He only proposed a coordinate system. Number line itself was a much later development. Descartes’ coordinates were a lot more abstract. If using the modern coordinate system is your criteria for analytic geometry, when was it finally established? What am I missing? Genuinely curious and happy to be completely wrong here. [1] https://en.wikipedia.org/wiki/Synthetic_geometry https://en.wikipedia.org/wiki/Synthetic_geometry [2] https://en.wikipedia.org/wiki/Analytic_geometry https://en.wikipedia.org/wiki/Analytic_geometry