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I took geometry more than 50 years ago. From my perspective, it was useless then as well. As far as I can tell, its goal was to illustrate the importance of ma

I took geometry more than 50 years ago. From my perspective, it was useless then as well. As far as I can tell, its goal was to illustrate the importance of mathematical proofs. Perhaps they are important to mathematicians, and I suppose they would be important if lots of high-school and college mathematics were potentially incorrect, so we needed a proof to reassure ourselves, but for most of us, even those who actively use mathematics, proofs are a waste of time. It would be better for students to become more comfortable with abstractions beyond multiplication.

naasking 5y ago
Real geometry is more important these days since computer graphics, photo and video editing and such are so common.
- chongli 5y ago
  The geometry of computer graphics is differential geometry of curves and surfaces. As a topic it requires a strong background in linear algebra and multi variable calculus. Not something a typical high school student has any preparation for.
  - naasking 5y ago
    Seems like a disingenuous take. There's a very obvious path to understanding the basics of computer graphics by introducing the basic shapes of geometry, particularly triangles for obvious reasons.
    - chongli 5y ago
      My interpretation of "computer graphics" was based on modern 3D graphics: transformation, lighting, texture mapping, animation, etc. High school geometry will get you the basics but that's a long way from the state of the art. See the rendering equation [1] for an example. [1] https://en.wikipedia.org/wiki/Rendering_equation https://en.wikipedia.org/wiki/Rendering_equation
      - naasking 5y ago
        Introduction to geometry is 2D. 3D comes much later. There's plenty of introductory material in 2D alone, even 2D computer graphics.
        chongli 5y ago
        Your original comment didn't say anything about introductory material. This whole discussion is about education to prepare students for university and beyond. No one is pursuing a career in computer graphics with only an introductory high school geometry background.
        naasking 5y ago
        No, this whole discussion is about K-12 education, which includes the very first introductions to geometry, and if you look at the existing geometry content from 2013 [1] it's mostly about 2D geometry, shapes, angles, rotations, translations, etc. That fits squarely in with 2D computer graphics. I also did emphasize "basic geometry" and "basic computer graphics" in my first reply to you. Finally, my first reply was disputing the claimed uselessness of geometry. It's very clear that it's far from useless these days, although some material is certainly less useful than it maybe used to be. [1] https://www.cde.ca.gov/ci/ma/cf/documents/mathfwgeometryjl.pdf https://www.cde.ca.gov/ci/ma/cf/documents/mathfwgeometryjl.p...

naasking 5y ago

Real geometry is more important these days since computer graphics, photo and video editing and such are so common.

chongli 5y ago
The geometry of computer graphics is differential geometry of curves and surfaces. As a topic it requires a strong background in linear algebra and multi variable calculus. Not something a typical high school student has any preparation for.
- naasking 5y ago
  Seems like a disingenuous take. There's a very obvious path to understanding the basics of computer graphics by introducing the basic shapes of geometry, particularly triangles for obvious reasons.
  - chongli 5y ago
    My interpretation of "computer graphics" was based on modern 3D graphics: transformation, lighting, texture mapping, animation, etc. High school geometry will get you the basics but that's a long way from the state of the art. See the rendering equation [1] for an example. [1] https://en.wikipedia.org/wiki/Rendering_equation https://en.wikipedia.org/wiki/Rendering_equation
    - naasking 5y ago
      Introduction to geometry is 2D. 3D comes much later. There's plenty of introductory material in 2D alone, even 2D computer graphics.
      - chongli 5y ago
        Your original comment didn't say anything about introductory material. This whole discussion is about education to prepare students for university and beyond. No one is pursuing a career in computer graphics with only an introductory high school geometry background.
        naasking 5y ago
        No, this whole discussion is about K-12 education, which includes the very first introductions to geometry, and if you look at the existing geometry content from 2013 [1] it's mostly about 2D geometry, shapes, angles, rotations, translations, etc. That fits squarely in with 2D computer graphics. I also did emphasize "basic geometry" and "basic computer graphics" in my first reply to you. Finally, my first reply was disputing the claimed uselessness of geometry. It's very clear that it's far from useless these days, although some material is certainly less useful than it maybe used to be. [1] https://www.cde.ca.gov/ci/ma/cf/documents/mathfwgeometryjl.pdf https://www.cde.ca.gov/ci/ma/cf/documents/mathfwgeometryjl.p...