
The Korbanos of the Shelosh Regalim are placed in this parsha of Pinchus. Let us take a few minutes to gain a deeper understanding of the Shlosh Regalim and then we will find an explanation to its relationship with Pinchus. Rashi in the previous parsha alludes to the Shlosh Regalim in the episode where Bilam hits his donkey three times because it alone sees the vision of the malach with an outstretched sword about to kill them and therefore refused to go any further. Chazal point out that the three times that Bilam hit his donkey corresponded to the Shlosh Regalim. The message was that you Bilam cannot be successful in the attempt to curse this nation who celebrates the Three Regalim. What is so significant of these Three Festivals that preserve the existence of this nation?
Another insight that must be addressed is the letter vov in the word בריתי שלוםwhich is called a Yud Ketiah a letter vov with a cut in the middle. Why did the Torah write this letter vov with a split in the letter which is not found anywhere else (see Baal Haturim). One of the greatest tragedies and disappointing setbacks in the history of Am Yisrael was the worshipping of the Aigel Hazahav. For this fallout, Hashem was ready to annihilate Yisrael would it not have been for the intervention and pleading of Moshe Rabbeinu on their behalf. Besides the יג מדות that Hashem bestowed to Moshe to protect Am Yisrael in times of kitrug, Hashem gave Yisrael the Shlosh Regalim. This is the reason why we find the mitzvah of Shlosh Regalim written in the Torah immediately after the chait of the Aigel Hazahav (Shmos 34, 18-23 see here the Ohr Chaim Hakadosh).
The Torah describes that the chait of the Aigel came about because Yisrael miscalculated the end of the forty days when Moshe Rabbeinu was supposed to descend from Har Sinai and bring to them the Luchos. וירא העם כי בשש משה לרדת מן ההר the nation saw that Moshe tarried in his returning to the camp. The sixth hour had already come without his appearance and therefore Moshe is presumed to be dead (Rashi Shmos 32,1). The meforshim explain that the fault of Am Yisrael was that they were too impatient and acted impetuously to make an idol to replace their leader. They could have waited a little more time and assume that they themselves miscalculated in the schedule of Moshe's return to them. However, the Airev Rav and the Satan put on them a heavy pressure and lachatz causing panic which is their regular routine and right away at the sixth hour they became obsessed in making an idol in Moshe's stead.
I heard in the name of the Yid Hakadoesh that the Shlosh Regalim came about in order to correct their mistake of the sixth hour. In Halacha there is a concept of Bittul beshishim. For instance, if milk falls into a meat pot and there is sixty times a quantity of meat against the milk then the halacha is that the milk that fell into the pot is considered negated and it is kosher. So too the sixth hour which instigated the aveirah of avodah zara must be corrected with the negation of sixty times which amounts to 360 hours. In this amount of hours we find that it corresponds to the total hours of the Shlosh Regalim. 7 days of Pesach equals 168 hours,7 days of Succos is another 168 hours, and one day of Shavuos is 24 hours totaling 360 hours. The Shlosh Regalim in which there is the mitzvah to be עולה רגל to the Beis Hamikdash and bring Korbanos is a fixing and correction of the chait of the Aigel the worshipping of avodah zarah. שלש פעמים בשנה יראה כל זכורך את פני האדון ה' אלקי ישראל. On Yom Tov a Yid rededicates his commitment and acknowledgement that Hashem alone is his master and no other deity. When the Aigel was made they said אלה אלהיך ישראל in contrast to every Yom Tov we declare Hashem is אלהי ישראל .
Interesting to note that a full circle is indeed 360 degrees. This is a standard convention in geometry and mathematics, derived from the Babylonian system of counting in base 60. The Babylonians, known for their astronomical observations, divided a circle into 360 parts, likely influenced by their base-60 number system and their understanding of the approximate number of days in a year. The Shlosh Regalim time period makes a full circle. The word חג also means circle as we will bring the Sfas Emes later on in the mamar. The word עגל is from the lashon of עיגול which means a circle. The tikkun for the Aigel is 60 times the bittul of the sixth hour and corrected and protected by the Shlosh Regalim.
The malach who was restraining Bilam's donkey from going forwards to which Bilam responded with hitting it three times, was sending the message that you cannot uproot Yisrael because they honor the Shlosh Regalim. The sefarim write that בלעם and בלק joined together with a united effort to arouse a kitrug on the chait of the Avodah Zara of the Aigel. Together with both names they contain the letters of .עמלק The sefarim tell us that the root cause of the Aigel was Amalek's vicious and unprovoked attack on Yisrael when they left Mitzrayim (see Sfas Emes Zachor (תרלה. Hashem through this malach was demonstrating to Bilam that he can't uproot the Three Regalim for they are the tikkun of the chait of the Aigel. When one takes away the Shlosh Regalim he removes with it our protection and atonement for worshipping avodah zarah.
With this we can understand the Chazal Pesachim 118 which says ואמר רב ששת משום רבי אלעזר בן עזריה כל המבזה את המועדות כאילו עובד עבודה זרה שנאמר אלהי מסכה לא תעשה לך וכתיב בתריה את חג המצות תשמר
Anyone who dishonors the Yamim Tovim is tantamount to worshipping avodah zarah. According to the above interpretation this comparison makes sense. The Moadim of the Torah are our protection from the grave aveirah of worshipping the Aigel. Remove the kovod for YomTov is to remove Yisrael's protection insurance from them bringing into the open the aveirah of a past avodah zarah that was extremely detrimental to Klal Yisrael.
We can now understand what is the meaning of the juxtaposition of Pinchus, who because of his meritorious act merited to be אליהו הנביא (Yalkut Pinchus, Pirkei D'Rav Eliezer 47), and the part of the parsha that deals with the korbonos of the Shlosh Regalim. Aliyahu Hanavi was known for his famous episode of ridding the false prophets from Yisrael who worshipped and
motivated members of Am Yisrael to embrace avodah zarah (Melachim 1,18). He had a grand showdown with them on Har Karmel bringing down a miraculous heavenly fire and consuming the Korban. Everyone acknowledged then ה' הוא האלקים and all the false prophets were killed.
Pinchus saved Am Yisrael from the aveirah of Avodah Zarah. He spiritually personified the Shlosh Regalim that also protect Am yisrael from the aveirah of the Aigel Hazahav. The gematriah of כרמל with the word 291 is identical to the gematriah ג' הרגלים . Pinchus in the form of אליהו הנביא had the power of the שלש רגלים to negate the tumah power of avodah zarah. Likewise בג' רגלים equals אלו פנחס אליהו. That Pinchus Aliyahu possessed the koach within himself of the Shlosh Regalim which is the tikkun and shemirah of the chait of the Aigel and the Sixth Hour. This is hinted in the letter vov ketiah in the word בריתי שלום which this vov is cut towards. It symbolizes the sixth hour which was the catalyst in the Chait HaAigle and has not yet reached its completion of atonement even though we have the Shlosh Regalim. The more we honor and appreciate the Yomim Tovim the more closer we get to putting the last amount of missing ink to complete the vov.
שפת אמת פסח תרסב שלש רגלים תחוג לי בשנה היינו לסבב כל השנה אל אלו הרגלים שהם יסוד ופנימיות של כל הזמנים. ושמעתי מפי מו"ז ז"ל כי חג מלשון מחוגה שהוא עגול ויש בה נקודה פנימיות כו'. היינו שיהי' סובב ובטל כל הימים אל החג שהוא הפנימיות כנ"ל:
This is what the passuk means when it says שלש שנים תחוג לי בשנה that the three Yomim Tovim should affect and encircle its influence over the rest of days in the year.