Top all-time · #5991
Jason Merrill
Personal blog · shapeoperator.commathprogramming
Jason Merrill writes Shape Operator, a personal blog at shapeoperator.com about math and programming. Since 2016, 13 different Hacker News readers have linked it 28 times, most often “Sunset Geometry (2016)”. It is still writing: the last post was on 2026-03-27, and you can follow it by feed.
Too few sampled comments (5) to say how often HN recommends it.?
Why HN links it
HN readers link Jason Merrill's blog for its geometric algebra posts, including applications to plane geometry and sunset geometry. Commenters also cite a floating-point bisection post and a critique of a dog magnetic-field claim.
Summarised by Claude from a sample of 5 HN comments that link here. Each comment is marked recommending, critical or neutral (citing without judging); how this works.
Most-linked posts?
- Sunset Geometry (2016)6 people · 9 mentions · first linked 2019-01-07
- Sunset geometry3 people · 10 mentions · first linked 2016-12-12
- Geometry, Algebra, and Intuition (2017)3 people · 4 mentions · first linked 2017-02-28
What Hacker News says?
It’s somewhat misleading/unfortunate to use angle measures as the basic characterization of an angle/rotation, when just trying to solve basic geometry / triangle measurement problems. It’s almost always easier to use a vector representation, written in terms of explicit coordinates if necessary (e.g. as a complex number). http://www.shapeoperator.com/2016/12/12/sunset-geometry/ Where angle measures and sines/cosine…
Comment linking /2016/12/12/sunset-geometry/
on “Big Picture of Calculus (2010) [video]”Submitted Geometry, Algebra, and Intuition (2017) as a story · 244 points
HN discussionAnything which repeats on some periodic interval (e.g. a signal which repeats in time) can be represented geometrically as being defined with respect to uniform motion around a circle (sometimes there are physical circles involved, and sometimes it’s just an abstract circle). Complex numbers (a two-part complex of a scalar part and a bivector part) and the complex logarithm/exponential are the natural formalism to u…
Comment linking /2016/12/12/sunset-geometry/
on “Why does e to pi i equal -1? (2015) [video]”Submitted Sunset Geometry (2016) as a story · 153 points
HN discussionThe better idea is to start with vectors. Adding vectors or scaling them is straight-forward. It’s trickier to figure out what it means to multiply or divide two vectors. The quotient of two vectors v / u should be some kind of operator which transforms one into the other (that is, when you multiply it by one, you get the other, ( v / u ) u = v ( u \ u ) = v , because we want multiplication to be associative). If th…
Comment linking /2016/12/12/sunset-geometry/
on “Why does e to pi i equal -1? (2015) [video]”Submitted Sunset Geometry (2016) as a story · 110 points
HN discussionHere, http://www.shapeoperator.com/2016/12/12/sunset-geometry/ http://geocalc.clas.asu.edu/pdf/OerstedMedalLecture.pdf http://geocalc.clas.asu.edu/pdf/GrassmannsVision.pdf
Comment linking /2016/12/12/sunset-geometry/
on “Why does e to pi i equal -1? (2015) [video]”Submitted Sunset Geometry (2016) as a story · 89 points
HN discussionThe nicest written-up example I know is https://www.shapeoperator.com/2016/12/12/sunset-geometry/ * * * As a relatively recent personal example I spent a few months (in bits and pieces) working out a bunch of metrical spherical geometry for myself without reference to past work, with points represented as displacement vectors to stereographically projected points at https://observablehq.com/@jrus/planisphere with th…
Comment linking /2016/12/12/sunset-geometry/
on “What is the inverse of a vector?”Submitted Sunset geometry as a story · 27 points
HN discussion>I suggest teaching vectors before trig. You can get the cosine and sine from the dot and cross products. What about geometric algebra instead? http://www.shapeoperator.com/2016/12/12/sunset-geometry/
Comment linking /2016/12/12/sunset-geometry/
on “Lessons I Wish I Had Learned Before Teaching Differential Equations (1997) [pdf]”Submitted Geometry, Algebra, and Intuition as a story · 4 points
HN discussionStart here http://www.shapeoperator.com/2016/12/12/sunset-geometry/
Comment linking /2016/12/12/sunset-geometry/
on “Lessons I Wish I Had Learned Before Teaching Differential Equations (1997) [pdf]”Submitted Sunset Geometry as a story · 3 points
HN discussionYou might like some of the other posts on the blog! I’ve written several other posts showing how Geometric Algebra can be used in plane geometry problems that would typically be treated with lengths and angles. Most recent post, which links to other parts of the series: https://www.shapeoperator.com/2019/02/10/proving-theorems-ab... An older post applying GA to the geometry of sunsets: https://www.shapeoperator.com/…
Comment linking /2016/12/12/sunset-geometry/
on “Geometry, Algebra, and Intuition (2017)”Submitted Geometry, Algebra, and Intuition as a story · 3 points
HN discussionhttps://news.ycombinator.com/item?id=12938727#12941658 Also see this nice recent blog post http://www.shapeoperator.com/2016/12/12/sunset-geometry/
Comment linking /2016/12/12/sunset-geometry/
on “An Introduction to Geometric Algebra”Submitted Geometry, Algebra, and Intuition as a story · 3 points
HN discussionI love to see more discussion of geometric algebra, but I have a few disagreements with this introduction: – Starting with standard linear algebra (vector spaces, matrices, etc.) leads to confusion. These ideas are best developed within the framework of geometric algebra, where their features can be easily proved / reasoned about, but only after the basic features of geometric algebra have been presented first. Afte…
Comment linking /2016/12/12/sunset-geometry/
on “An Introduction to Geometric Algebra”Submitted Sunset Geometry (2016) as a story · 2 points
HN discussionPerhaps start with https://www.shapeoperator.com/2016/12/12/sunset-geometry/ for a concrete example.
Comment linking /2016/12/12/sunset-geometry/
on “Why is Maxwell's theory so hard to understand? (2007) [pdf]”Submitted Geometry, Algebra, and Intuition as a story · 2 points
HN discussionThat sounds like the traditional method of learning math. I was wondering if we could leverage technology and our experiences with teaching/learning the formal systems of programming languages to make more math more accessable. For instance, I'm thinking this little instance of geometric algebra: http://www.shapeoperator.com/2016/12/12/sunset-geometry/ ...might be easier for me to understand if I could use Haskell t…
Comment linking /2016/12/12/sunset-geometry/
on “Course Notes – J.S. Milne”Submitted Optimizing a Kakuro puzzle solver in Julia as a story · 1 points
HN discussionWhat is your background/perspective? For introductory motivation, check out https://www.shapeoperator.com/2016/12/12/sunset-geometry/ And perhaps follow up with the GA for Computer Science book, or if you like (or want to learn about) Newtonian mechanics, try Hestenes’s book New Foundations for Classical Mechanics . For people with a mathier background, I would recommend https://arxiv.org/abs/1205.5935
Comment linking /2016/12/12/sunset-geometry/
on “Seven-Dimensional Cross Product”This behavior can actually be turned around and exploited to do some calculations to full precision, using algorithms that look like they would infinite loop: http://www.shapeoperator.com/2014/02/22/bisecting-floats/
Comment linking /2014/02/22/bisecting-floats/
on “Mean of two floating point numbers can be dangerous”Discussed in 2020 (160 comments) https://news.ycombinator.com/item?id=22276468 and 10 months ago (44 comments) https://news.ycombinator.com/item?id=32736851 A good blog post on the seeming ridiculousness of the claim: https://www.shapeoperator.com/2020/02/15/how-to-lie-with-uni...
Comment linking /2020/02/15/how-to-lie-with-units/
on “Dogs are sensitive to small variations of the Earth’s magnetic field”
