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There are three pairs of names for the sun and moon in Hebrew, corresponding to the essential male and female archetypes of the three lower worlds. The combined numerical value of the three names of the moon [yareiach - Beriah, levanah - Yetzirah, sahar - Asiyah] (the female archetype) is 570, which equals 30 x 19, 19 being the value of חוה (Eve). The average value of the three names is 190, which equals צלע (the "side" or "rib" from which Eve was created); this number is the triangle of 19, Chavah. The average menstrual cycle (עונה בנונית) is 30 days long.

The combined numerical value of the three names of the moon [yareiach, levanah, sahar] (the female archetype) is 570, which equals 30 x 19, 19 being the value of חוה (Eve). The average value of the three names is 190, which equals צלע (the "side" or "rib" from which Eve was created); this number is the triangle of 19, Chavah. The average menstrual cycle (עונה בנונית) is 30 days long.

There are three pairs of names for the sun and moon in Hebrew, corresponding to the essential male and female archetypes of the three lower worlds. The combined numerical value of the three names of the moon [yareiach - Beriah, levanah - Yetzirah, sahar - Asiyah] (the female archetype) is 570, which equals 30 x 19, 19 being the value of חוה (Eve). The average value of the three names is 190, which equals צלע (the "side" or "rib" from which Eve was created); this number is the triangle of 19, Chavah. The average menstrual cycle (עונה בנונית) is 30 days long.

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R. Yitzchak Ginsburgh

For a kabbalistic explanation, R. Ginsburg connects the word for rib with womanhood in his The Mystery of Marriage (p. 275):

The combined numerical value of the three names of the moon [yareiach, levanah, sahar] (the female archetype) is 570, which equals 30 x 19, 19 being the value of חוה (Eve). The average value of the three names is 190, which equals צלע (the "side" or "rib" from which Eve was created); this number is the triangle of 19, Chavah. The average menstrual cycle (עונה בנונית) is 30 days long.

R. Yitzchak Ginsburgh

For a kabbalistic explanation, R. Ginsburg connects the word for rib with womanhood in his The Mystery of Marriage (p. 275):

The combined numerical value of the three names of the moon [yareiach, levanah, sahar] (the female archetype) is 570, which equals 30 x 19, 19 being the value of חוה (Eve). The average value of the three names is 190, which equals צלע (the "side" or "rib" from which Eve was created); this number is the triangle of 19, Chavah. The average menstrual cycle (עונה בנונית) is 30 days long.

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There are many explanations to the significance of creating Eve from Adam's rib. By the way, it's not a universal opinion that "tzela" should be translated as "rib" (Hazal have also transalted it as "side," which works with the midrash of them being originally joined together). Going with the "rib" translation, here are a few explanations.

Bereshit Rabbah 18:2

רבי יהושע דסכנין בשם ר' לוי אמר ויבן כתיב, התבונן מאין לבראתה אמר לא אברא אותה מן הראש שלא תהא מיקרת ראשה, לא מן העין שלא תהא סקרנית, ולא מן האוזן שלא תהא צייתנית, ולא מן הפה שלא תהא דברנית, ולא מן הלב שלא תהא קנתנית, ולא מן היד שלא תהא ממשמשנית, ולא מן הרגל שלא תהא פרסנית, אלא ממקום שהוא צנוע באדם אפי' בשעה שאדם עומד ערום אותו המקום מכוסה, ועל כל אבר ואבר שהיה בורא בה היה אומר לה תהא אשה צנועה אשה צנועה, אעפ"כ (משלי א) ותפרעו כל עצתי, לא בראתי אותה מן הראש, והרי היא מיקרת ראשה שנאמר (ישעיה ג) ותלכנה נטויות גרון, ולא מן העין והרי היא סקרנית שנאמר (שם /ישעיהו ג'/) ומסקרות עינים, ולא מן האוזן והרי היא צייתנית שנאמר (בראשית יח) ושרה שומעת פתח האהל, ולא מן הלב והרי היא קנתנית שנאמר (שם /בראשית/ ל) ותקנא רחל באחותה, ולא מן היד והרי היא ממשמשנית שנאמר (שם /בראשית/ לא) ותגנוב רחל את התרפים, ולא מן הרגל והרי היא פרסנית שנאמר (שם /בראשית/ לד) ותצא דינה.

...He [God] said, "If I will create her from the head, she will be lightheaded. If I will create her from her eyes, she will be overly curious. If I create her from the ears, she will always be listening to gossip, causing much strife when she spreads news about others' affairs. If I create her from the mouth, she will be talkative. If I create her from the heart, she will be jealous. If I create her from the hands, she will constantly handle things. If I create her from her feet, she will be footloose. Instead, she should be created from a place that is modest in man even when he is naked and yet is still covered...[then there is more midrash on the body parts man and woman share].

Regarding this midrash the Meam Loez comments:

Everything is influenced by the source from which it was created. God therefore arranged things so the woman was not created from any place that would have an adverse influence.

God wanted woman to be as perfect as possible, and not to have any undesirable traits. He therefore created her from a place which could not have any adverse effect on her personality. He wanted her to be intrinsically free of all adverse traits.

Meam Loez

The Meam Loez also offers his original (albeit less palatable) opinion as to the reason of the rib:

He [a man] should also realize that woman was created from hard bone; she is therefore hard and stubborn. Man was created from soft earth; he is thus more flexible.

Targum Yonathan 2:21-22

ורמא יי אלהים שינתא עמיקתא עלוי אדם ודמך ונסיב חדא מעלעוהי הוא עלעה תליסרית דמן סטר ימינא ואחד בבשרא: ובנא יי אלהים ית עלאה דנסב מן אדם לאיתתא ואתיה לות אדם

[Man has fifteen ribs on each side.] ...The one that God took to create the woman was the thirteenth rib on the right side. Adam was created with an extra rib, so that when the woman was created, no part of his body was lacking.