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(1.) is true only if the line is straight.
(2.) is somewhat imprecise, but close enough for a working definition.

And, just for completeness, a plane is a flat surface. I just took a look at the...

And that's the reason why you cannot have a smiling edge lay on a flat hone. If you can make it with a single piece of paper you'd be done.


If I understand correctly your proposition, the part...

Uhm, no, the statement is correct, your understanding of math isn't. A 'curved plane' is called 2-dimensional space or surface and generally is not made from interjections of planes. If the...

Math time: the intersection of two planes is a straight line.

That means that no razor with a smile can have the whole edge on the hone at a single moment. The bigger the smile the bigger the...