Geometry: all circles are ellipses; all squares are rectangles; congruent figures are similar -- it ain't necessarily so
He, he I came across this tidbit on plane figure: 'congruence' cp 'similarity'.
The related concept of similarity applies if the objects have the same shape but do not necessarily have the same size. (Most definitions consider congruence to be a form of similarity, although a minority require that the objects have different sizes in order to qualify as similar.)
No citation given for 'a minority', so a black mark to wikipedia. Here's some (but I fear they might just be sloppy wording):
Similar figures mean when two figures are of the same shape but are of different sizes.
When a shape is enlarged, the image is to the original shape. It is the same shape but a different size. [The BBC, no less]
There's an answer at Quora.com "‘congruent but not similar’ is an impossibility" -- dated in the past year. Everything my spambox has received from Quora in the past few years has been balderdash, so this is the strongest confirmation.
In ordinary English congruent means 'the same shape', similar means 'resembling but not the same'. But mathematicians are known for playing games with ordinary English, so YMMV.
Quote from dandl on July 21, 2024, 10:20 amIn ordinary English ...
Yeah. Ordinary English 'similar' means (probably) not exactly the same. If you described twins as 'similar' when you knew they were identical, you'd be breaking some Gricean maxim.
So if you talk about ellipses when you mean exclusively circles, that's also a solecism. Furthermore if talking about both, I'd expect explicit sth like 'ellipses, including circles'.
In any case, databases hold representations, not circles/ellipses. The representation for a circle might be [**] transformable to the same representation as an ellipse; describing that as 'a circle is an ellipse', the copula is doing a solecism-level of heavy lifting.
[**] I'll guess somebody might object to my "might be" -- surely always can be? Well no: the POSSREP might include constraints requiring the eccentricity greater than zero.
Quote from AntC on July 21, 2024, 9:52 amThere's an answer at Quora.com "‘congruent but not similar’ is an impossibility" -- dated in the past year. Everything my spambox has received from Quora in the past few years has been balderdash, so this is the strongest confirmation.
Uh oh. I've written almost 10,000 answers on Quora.
But you're right -- it's mostly balderdash. Except my answers; they're perfect exemplars of shining correctness.
It's also an entertainment site, like the rest of the Internet. Best not to trust any of it.
Quote from Dave Voorhis on July 22, 2024, 5:48 pmQuote from AntC on July 21, 2024, 9:52 amThere's an answer at Quora.com "‘congruent but not similar’ is an impossibility" -- dated in the past year. Everything my spambox has received from Quora in the past few years has been balderdash, so this is the strongest confirmation.
Uh oh. I've written almost 10,000 answers on Quora. ...
Thanks Dave, that's why I said "dated in the past year". It was you (a long time ago) persuaded me to go looking at Quora. Very soon after that it went steeply down hill. Nowadays all I get is spam from people asking about emigrating to New Zealand (or more recently emigrating from NZ, go figure).
I think your answers weren't on geometry topics (?)
There is no dependable database forum left on the internet except this.
Says everything about how much the world needs dependability.
About the geometry : If you decree an ellipse to satisfy A>B, then no circle is an ellipse. If you decree an ellipse to satisfy A>=B, then all circles are ellipses. To claim without proof that either decree must be wrong, seems like a solecism itself to me.
Quote from Erwin on August 9, 2024, 5:40 pmThere is no dependable database forum left on the internet except this.
Says everything about how much the world needs dependability.
I suspect the fact that most people receive exactly the same paycheque every payday whether the information systems they build or use are dependable or not has a lot to do with the fact that dependability is a low, low priority.
When the C2 wiki broke I knew we were all doomed. The Internet is for hook-ups, pile-ons and endless ads, not for the likes of us.
But there are tiny corners of reason and hope, for now.
Quote from dandl on August 10, 2024, 12:46 amWhen the C2 wiki broke I knew we were all doomed. The Internet is for hook-ups, pile-ons and endless ads, not for the likes of us.
But there are tiny corners of reason and hope, for now.
Indeed.
There are pockets of goodness, but they're mostly kept small and hidden.