Question: Are only four-cornered garments obligated in tzitzis?
Answer: Sort of. Three-cornered garments are not obligated. Five- or more-cornered garments are obligated, but one may only put four fringes on them, and the fringes should be spread out to the farthest corners.
Question: What if a corner of a garment is cut diagonally – is it now considered to have one less corner?
Answer: Au contraire! – Now the garment has one more corner (i.e. if the cut edge appears to have two corners on it alone)!
Question: Based on the above, if a four-cornered garment had one of its corners diagonally cut, it would be obligated before and after the cut was made. But what if the same thing happened to a three-cornered garment – i.e. one corner was cut and now the garment appears to have four corners - do we say that a mere diagonal cut can change the status of the garment from exemption to obligation? Answer: That is a ‘machlokes’ (dispute). Some say that in order for a three-cornered garment to be transformed into an obligated four-cornered one, one of the corners must be split into two halves by a very long cut, i.e. perpendicular to a diagonal cut. Only then would the garment really have four “corners” to it.
Question: What if one of the corners of a four-cornered garment was rounded – does it lose its status of obligation?
Answer: If it is permanently rounded by cutting the material, then, yes, the status changes. If it is merely sewn into a round shape, but the material itself is still square, then it is still considered to be four-cornered.
Question: What if the garment is made of cloth, but it has square-shaped patches made of leather sewn onto its corners? (Note: Leather is not considered to be a garment at all and is by itself not obligated in tzitzis.)
Answer: The answer is surprising: Not only is the garment still obligated in tzitzis in that case – because the main material of the garment is cloth (note: this is true even up to half of leather!) - but even if the cloth itself is completely rounded and only the leather patches make it square, we still consider it to be a four-cornered cloth garment!
Question: Here is a question that “ties together” everything we have learned in this siman: What if one tied three tzitzis-fringes on a three-cornered garment (which is not obligated) and then created a fourth corner; can he now simply add a fourth fringe onto it?
Answer: You would think so. However, there is a principle that a mitzvah object must be initially made in a kosher state to be valid. Since at the time that the first three fringes were tied, it was not a kosher talis, those fringes are invalid and remain so indefinitely even when a fourth corner is added. One would need to untie the three fringes and re-tie them again in order for them to be kosher. (Ed: This is analogous to putting schach on a sukkah frame before the walls are made, or bending branches from a tree onto a sukkah and then cutting the branches off. Since the schach was invalid when it was first put on, it must be removed - i.e. lifted up - and replaced after the invalidating factor has been rectified.)