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hoseja

Shouldn't that be obvious from the transformation matrices? (I'm just vaguely sure this is true.)

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Ah, the mathematician's "obvious", where it clearly isn't :)

I am no mathematician but as far as I remember a shear matrix is just half of a rotation matrix (in 2D).

as the article states, R = STS, where S is the same shear in both factors.

Question at a mathematical seminar: "Isn't it obvious that [...]?", the speaker turns to blackboard, writes furiously for 5 minutes muttering to himself, then replies "Yes it is!"

Sounds about right; any code I could write in 5 minutes is necessarily trivial, so I assume similar for other professions that don't have hard time limits.

Writing for for 5 minutes is much easier than thinking for 5 minutes.

"Obvious" means you know it without thinking.

In a math lecture context obvious is intuitively true, five minutes on the blackboard is "trust (your gut) but verify".

Not everything pans out the way even the best think - and the very best are notorious for "knowing" results in a flash .. but having to diddle about to produce a logical chain that "proves" that flash for minute, hours, days and sometimes years or a century after their death..

That get us to the obvious theorems that are actually false https://math.stackexchange.com/questions/820686/obvious-theo...

To be fair many of those "obvious truths" are rapidly discounted by the kinds of teenagers that go on to become university core math students.

Fractal surface areas, the re-order of terms in an infinte series, infinite hotel questions, etc. were all high school puzzles in the 80s in my part of remote Australia so I can't imagine them stumping or confusing a university math lecturer.

This is domain where one letter variables is not only the norm but expectation.

When reading the title I thought that too (maybe not “obvious”, but “unsurprising”), but what’s neat is that each pixel can be preserved 1:1, which I hadn’t expected.

I thought it was super mind blowing to learn that percentages were reversible, apparently that's obvious to people who know math well.

I am not sure why you are being downvoted. I have been doing a project with Homogeneous Transform Matrices recently and also assumed that this was "obvious" since the shear diagonal lives in the rotation part of the matrix. Still, it's a very neat trick and I appreciate the OP for posting it!

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