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> The only way to create a proper circle is to have a raster image like the one above. The raster image won't be a circle, it'll be a circle projected onto a s

> The only way to create a proper circle is to have a raster image like the one above. The raster image won't be a circle, it'll be a circle projected onto a square or rectangular grid. But, just like with the Bezier curves, nobody will notice. I remember the first week of Geometry, they told us that the drawings of squares and circles and whatnot printed in the textbook are not intended to be accurate, so don't bother measuring them to get the answer. The circle represents a circle, it is not a circle. Wait til I tell you about this painting of a French pipe I saw one time.

gerdesj 3y ago
Ceci n'est ... perhaps? There was a Greek bloke who had a thing about perfection and geometry. Eclad or something similar (OK: Euclid). At what point does the perfect approach reality or vice versa? The pipe in question might not be French - the painting was painted by a French person but you cannot imply the country of the pipe itself on that basis without additional evidence!
- bombcar 3y ago
  Euclid with diagrams is modernism! The original texts didn’t have them.
ilove_banh_mi 3y ago
what if someone told you the painting's subject matter is not a Belgian pipe
- armoredkitten 3y ago
  Clarifying that the non-pipe is a Belgian non-pipe and not a French non-pipe reminds me of the joke with Sartre: Jean-Paul Sartre was sitting in a cafe when a waitress approached him: "Can I get you something to drink, Monsieur Sartre?" Sartre replied, "Yes, I'd like a cup of coffee with sugar, but no cream". The waitress left, but returned a few minutes later and said, "I'm sorry, Monsieur Sartre, we are all out of cream -- how about with no milk?"
TeMPOraL 3y ago
> I remember the first week of Geometry, they told us that the drawings of squares and circles and whatnot printed in the textbook are not intended to be accurate, so don't bother measuring them to get the answer. I considered, and to this day consider, inaccurate figures in textbooks to be sloppy job by lazy people. Sure, measuring the solution off a drawing is (in math classes) missing the point of the exercise, but at the same time, humans process knowledge holistically, so inaccurate drawings will interfere with gaining an intuitive understanding of a problem space. I mean, if you were using software to chart some data you want to "get a feel for", would you be fine with software introducing arbitrary errors just because "Ceci n'est pas une pipe" or whatever?
- karaterobot 3y ago
  Looking back as a grown-up, I'm sure the teacher just said this to head off anyone considering cheating by making them think it would be a waste of time. The illustrations did look pretty close to accurate to me.
- ElectricalUnion 3y ago
  > inaccurate figures in textbooks Sometimes it's not about being accurate, sometimes it's about the figures in the textbook representing unrepresentable, impossible situations on whatever geometry you're operating on. say euclidean geometry. Casual things like triangles where the sum of internal angles doesn't match π. Triangles where the sum of length of the two smaller sides is larger that the larger side. Being able to reason about what are supposed to be the constraints of a otherwise impossible system is valuable in itself.
  - TeMPOraL 3y ago
    I do agree with that, and I understand there are many things that just plain cannot be represented accurately on paper - whether through drawings or symbolically. But once you draw an illustration of some thing, I'd expect everything about the drawing to be depicting the real thing as accurately as possible, unless explicitly marked otherwise. If you're not doing that, you may as well skip the illustration entirely, because it confuses things more than it helps.

gerdesj 3y ago

Ceci n'est ... perhaps? There was a Greek bloke who had a thing about perfection and geometry. Eclad or something similar (OK: Euclid). At what point does the perfect approach reality or vice versa? The pipe in question might not be French - the painting was painted by a French person but you cannot imply the country of the pipe itself on that basis without additional evidence!

bombcar 3y ago
Euclid with diagrams is modernism! The original texts didn’t have them.

ilove_banh_mi 3y ago

what if someone told you the painting's subject matter is not a Belgian pipe

armoredkitten 3y ago
Clarifying that the non-pipe is a Belgian non-pipe and not a French non-pipe reminds me of the joke with Sartre: Jean-Paul Sartre was sitting in a cafe when a waitress approached him: "Can I get you something to drink, Monsieur Sartre?" Sartre replied, "Yes, I'd like a cup of coffee with sugar, but no cream". The waitress left, but returned a few minutes later and said, "I'm sorry, Monsieur Sartre, we are all out of cream -- how about with no milk?"

TeMPOraL 3y ago

> I remember the first week of Geometry, they told us that the drawings of squares and circles and whatnot printed in the textbook are not intended to be accurate, so don't bother measuring them to get the answer. I considered, and to this day consider, inaccurate figures in textbooks to be sloppy job by lazy people. Sure, measuring the solution off a drawing is (in math classes) missing the point of the exercise, but at the same time, humans process knowledge holistically, so inaccurate drawings will interfere with gaining an intuitive understanding of a problem space. I mean, if you were using software to chart some data you want to "get a feel for", would you be fine with software introducing arbitrary errors just because "Ceci n'est pas une pipe" or whatever?

karaterobot 3y ago
Looking back as a grown-up, I'm sure the teacher just said this to head off anyone considering cheating by making them think it would be a waste of time. The illustrations did look pretty close to accurate to me.
ElectricalUnion 3y ago
> inaccurate figures in textbooks Sometimes it's not about being accurate, sometimes it's about the figures in the textbook representing unrepresentable, impossible situations on whatever geometry you're operating on. say euclidean geometry. Casual things like triangles where the sum of internal angles doesn't match π. Triangles where the sum of length of the two smaller sides is larger that the larger side. Being able to reason about what are supposed to be the constraints of a otherwise impossible system is valuable in itself.
- TeMPOraL 3y ago
  I do agree with that, and I understand there are many things that just plain cannot be represented accurately on paper - whether through drawings or symbolically. But once you draw an illustration of some thing, I'd expect everything about the drawing to be depicting the real thing as accurately as possible, unless explicitly marked otherwise. If you're not doing that, you may as well skip the illustration entirely, because it confuses things more than it helps.