5 ms·
I think the line integral of curvature (changes sign based on concave / convexness) along perimeters remains the same under cutting / pasting; and it's differen
by nikki93 7y ago
I think the line integral of curvature (changes sign based on concave / convexness) along perimeters remains the same under cutting / pasting; and it's different for squares and circles, so doesn't work out.
- rocqua 7y agoSeems like a nice approach, but is the line integral of curvature along the perimeter of a square defined? The corners are infinitely small line segments with infinite curvature. Perhaps this works for squares with slightly rounded-off corners.
- nikki93 7y agoThe square is defined as a union of lines, and the line integral of a whole shape is the summation of that of the curves it is a union of with open intervals not including the "corners" (points of 'infinite curvature' as you say). I think this definition would suffice because we just need to show that the sum is closed over cutting, no?