Add Sefer Hachinuch method. Organize top into sections. Links to diagrams.
*The pesukim in Shalach <ref>Bamidbar 15:38 </ref> introduce the mitzvah of [[Tzitzit]] and among them is one that mentions the requirement to have a string of the Techelet color.
"דבר אל בני ישראל ואמרת אלהם ועשו להם ציצת על כנפי בגדיהם לדרתם ונתנו על ציצת הכנף פתיל תכלת"
*The Mishna (menachot 38a) writes
clearly that wearing [[Tzitzit]] without Techelet also fulfills the mitzvah of [[Tzitzit]] (while lacking a part of the mitzvah). This is codified in the Rambam ([[Tzitzit]] 1:3).
*From the end of the era of the sages of the Gemara Techelet became unavailable and extinct from common practice. However, in the last century and a half many have investigated this lost dye and some claim to have rediscovered it. The halachic question is how to deal with the dyes which some have claimed to be the real Techelet of the Torah.
*Rav Hershel Schachter in Ginat Egoz ([[Siman 2]]) writes that there is very little reason not to wear the [[Tzitzit]] because of a doubt that perhaps it is the correct Techelet. He addresses the fact that the minhag is to wear a white garment with white strings, but says clearly that there’s no reason that this minhag should override a possibility to fulfill a biblical mitzvah. Furthermore, the Bet HaLevi (Sh”t Bet HaLevi 42) who says that there’s a prohibition of detracting from the מצות by fulfilling a mitzvah in a inferior way but that since a positive mitzvah overrides a negative one, there’s still reason to wear [[Tzitzit]] without Techelet because one still fulfills a positive mitzvah. Extending this further, Rav Schachter writes that if a person owns Techelet then it becomes possible to fulfill the positive mitzvah and negative one simultaneously and therefore one wouldn’t be allowed to use a positive mitzvah to override a negative one. To see how Rav Schachter ties the Techelet [[Tzitzit]] see here [http://www.tekhelet.com/diagrams/Schachter7TyingDiagram2.pdf www.tekhelet.com] For a detailed how-to, see [https://www.mywesternwall.net/2019/04/02/techeiles-how-to-tie-tzitzis-like-r-hershel-schachters-method.html mywesternwall.net].
The Radziner in Petil Techelet summarizes the dispute:
#Rambam holds that one string out of eighth are techelet.<ref>[https://www.sefaria.org/Mishneh_Torah%2C_Fringes.1.6/ Rambam Halachot Tzitzit 1:6]</ref> Sefer Hachinuch, Maggid Meisharim, Mabit, Maharam Ibn Gabay, Sefer Charedim, Levush, Gra, Sefer Hakaneh, and Arizal agree with the Rambam. Radziner in Petil Techelet ch. 6 ends up following the Rambam but says one has what to rely upon to follow either of the other opinions. Ben Ish Chai (Noach n. 17) and in [http://www.hebrewbooks.org/pdfpager.aspx?req=41237&st=&pgnum=101 Od Yosef Chay (Vaera n. 3)] holds like the Rambam. [https://www.ykr.org.il/question/1629 Rav Yonatan Mazuz] agrees.
#Raavad holds that one string out of four (two out of eight) is techelet.<ref>[https://www.sefaria.org/Hasagot_HaRaavad_on_Mishneh_Torah%2C_Fringes.1.6.1/ Raavad on Rambam Halachot Tzitzit 1:6]</ref> Aruch (Techelet) agrees with the Raavad. He cites the Sefer Haitur, Sefer Machriya, Tur, Rabbenu Yerucham, Shulchan Aruch Harav who agree. Smag has safek like Tosfot or Raavad.
#Rashi and Tosfot hold that four strings out of eighth are techelet.<ref>[https://www.sefaria.org/Rashi_on_Menachot.38a.4.1 Rashi on Mishna of Menachot 38a]</ref> [https://www.yutorah.org/sidebar/lecture.cfm/788501/rabbi-hershel-schachter/hilchos-tzitzis/ Rav Schachter ("Hilchos Tzitzis" beginning)] holds like Rashi and Tosfot and recommends all Ashkenazim to follow this method due to the plethora of sources advocating it (Baal haIttur, Tur, Shulchan Aruch, etc.).
The Rambam maintains that there should be between 7-13 links (chulyot) and that each link should have 3 winds (krichot). In the closest link to the garment, the first wind should be white, while the other two winds of that link should be techelet. In the farthest link from the garment, the final wind should be white, while the other two winds of that link should be techelet. All other links contain only techelet.<ref>[https://www.sefaria.org/Mishneh_Torah%2C_Fringes.1?lang=bi Rambam, Halachot Tzitzit Chapter 1]</ref>
The Raavad holds that there should be 4 links and that each link has 7 winds. Each link is separated by a knot. The winds of each link should alternate white and techelet, the first and last wind of each link being white. The Raavad dictates that the link closest to the edge of the garment and the two links farthest from the garment must follow the alternating pattern. However, the unmentioned link can either be all white or the alternating white and techelet pattern.<ref>[https://www.sefaria.org/Hasagot_HaRaavad_on_Mishneh_Torah%2C_Fringes.1.7.1?lang=bi Raavad on Rambam Halachot Tzitzit 1:7]</ref>