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The commandment to attach tzitzit to the four corners of our garments is a Torah obligation, as per Bamidbar 15:38 and Devarim 22:12.

Our Sages of blessed memory ruled that a garment that does not have four corners is exempt from the obligation of tzitzit.

Later, when the four-cornered garment started becoming a less-popular mode of clothing, Jewish males began wearing a special four-cornered garment known as the tallit katan in which to attach tzitzit to, so the mitzvah would not go extinct.

My question is thus: what is considered a four-cornered garment? I assume something that has four corners along the bottom, but what about dress shirts? Technically speaking, they have two corners at the bottom hem, two corners at each cuff and two corners at the collar. Why are those corners on the cuffs and collar exempt from tzitzit?

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    Something tells me that we have at least one MY question that answers this. I have trouble finding it, now. – DanF Apr 4 '17 at 20:56
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    Thank you everyone. If I could accept every answer I would. :) – ezra Apr 4 '17 at 21:49
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The Mishna Brura on Orach Chayim 10:12 writes regarding this question the following

(Source provided by Sefaria.org)

לו) הואיל ואין וכו' - דהנה הב"י כתב יש לדקדק במלבושים שלנו שיש להם ב' כנפות סמוך לצואר וב' כנפות סמוך לארץ למה אין מטילין בהם ציצית ותירץ ע"ז כמה תירוצים ודחה אותם הד"מ ואמר הוא טעם להמנהג דמאחר דמצות ציצית הוא לכתחלה שיחזיר ב' לפניו וב' לאחריו ומלבושים שלנו הם כל הד' כנפות לפניו וא"א להלבישן בענין אחר אין חייבין בציצית וזהו מה שכתב הואיל ואין כנפיהם עשויין וכו

The Beis Yosef writes that there is to point out that why don't we put Tzitzis our clothes which have two corners near the neck (i.e. the collar) and two corners near the ground and provides several answers for this and which the Darchei Moshe rejects and explains the reason for the practice is since the Mitzva of Tzitzis is ideal when one has two (tzitzis) in front of him and two behind him and our clothes all four of the corners are in front of the individual and it is impossible for him to wear it in another manner (therefore) it is not obligated in having tzitzis on it and this is what he(the Rema [ibid.]) wrote "Since the corners are not made etc. (in a manner which has two tzitzis in the front and two in the back)"

Hope this is insightful

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The issue is whether the sides of the garment are open.

Halachipedia, “Other garments” (6) says

If the majority of a garment's side is open then it must have Tzitzit, but if a minority of a garment's side is open then it is exempt from having Tzitzit.

Aish.com elaborates this and says

Only a four-cornered garment is required to have Tzitzit.  A poncho, for example, requires Tzitzit. A regular button-down dress shirt does not require Tzitzit, because it only has two "corners" (in the front). Similarly, a t-shirt does not require Tzitzit, as it has no corners. However, if one would cut a slit up the sides of the t-shirt (so that a majority of the side is "open"), that would in effect create "four corners," and the t-shirt would require Tzitzit.

See the diagram there.

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Tzitzis must have the strands on the four (squared) corners of a rectangular garment. The corners of the sleeves and collars of the shirt or suit, besides not being 90 degrees, are not considered the corners of the garment. As an example, the suit jacket vents are usually rounded and do not extend long enough up the back to allow tzitzis to be attached.

An example that some people use would be the Mexican Serape or the Roman toga which are like a sheet with four rectangular corners when spread out.

Tallis/Tzitzis

That is, all garments of a certain size or larger, which have at least four corners, must have strings known as tzitzit attached. The original requirement was to have a blue thread among the white threads; however, since the precise shade of blue is no longer known and the source of the dye used, only the white threads are used (except among certain chasidic groups that claim to know the dye formula).

Since the normal clothing in our time does not have four square corners, traditional Jews wear a garment that is specifically made to have four corners so that the mitzvah can be fulfilled.

Wrapping Ourselves Blindly

The Gemara in Shabbos 147a and Menachos 41a implies that during the times of the Talmud (and presumably in earlier times as well), most people wore clothing that consisted of a single four-cornered garment that was wrapped around the body.

E.g.,Rabbi Aryeh Kaplan, The Tallith Katan in “Tzitzith: A Thread of Light,” NCSY/Orthodox Union (hereinafter, The Tallith Katan).

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