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Is there a source that compiles the different times that polygons and other non-polygons that come up in tanach/gemara? I'm looking to fine any place where quadrilaterals, pentagons, hexagons etc. and circles, parabolas etc. appears in Tanach/Gemara.

For example, the concept of a circle is discussed with regards to tzaddikim sitting in Olam Haba.

Does anyone have a compilation of sources?

user16803
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  • Not really helpful to this question, but possibly of additional interest: https://judaism.stackexchange.com/q/10443 – msh210 Feb 25 '18 at 22:18
  • This is an amazing question. I wonder if someone will find conics other than circles lines and points – SAH Feb 26 '18 at 00:09
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    Gemara Sukkah has plenty of discussion around different shapes of sukkahs and various geometric calculations (e.g area, etc.) around daf 10 or so IIRC. It also brings of Solomon's pool from the 1st Beis HaMikdash and the calculation of it's area. – Fei23 Feb 26 '18 at 00:38
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    There's this nice geometrical problem of the tablets in Bava Batra 14b http://halakhah.com/bababathra/bababathra_14.html – Kazi bácsi Feb 26 '18 at 09:09

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Bava Batra 164b quotes the following beraita from Tosefta Nega'im:

תנו רבנן בית עגול דיגון טריגון פנטיגון אינו מטמא בנגעים טטריגון מטמא בנגעים

Our Rabbis taught: A house which is circular, two-sided*, triangular or pentagon-shaped is not susceptible to nega'im-impurity. If it is quadrilateral-shaped, it is susceptible to nega'im-impurity.

*Presumably at least one of the two sides is curved.

Joel K
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B"N, I shall place the exact verse later.

In last week's Shabbat parsha, Tetzaveh, when discussing the choshen, it says that it should be made as a double square.

A square shape is mentioned for the altar.

Similarly, I believe that in Melachim (Kings) I, there is mention about how the stones for the Bet Hamikdash were made as perfect squares. (Umm. is there such a thing as an "imperfect square?)

DanF
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  • Does it say perfect square or perfect rectangle? – DonielF Feb 27 '19 at 19:56
  • @DonielF My hunch is that the word ravu'a means "square" and not just "four-sided figure". One thing is certain. The mizbe'ach was a square, but not a cube. Shemot 30:2 says that it should be one amah in length and one amah in width. I assume that the word ravu'a implies that the length and width should be at right angles. Also, Shemot 28:16 says that the choshen was 1 zeret in length & 1 zeret in width. So that's also square. – DanF Feb 27 '19 at 23:12
  • All squares are rectangles, and all rectangles are quadrilaterals, but not all quadrilaterals are rectangles, nor are all rectangles squares. I’m pretty sure רבוע specifically refers to rectangles, as otherwise the passuk by the Choshen wouldn’t have to say 1 zeres by 1 zeres; it could just say it’s 1 zeres square (and the same argument by the Mizbeiach). – DonielF Feb 28 '19 at 00:05
  • @DonielF I'm missing your point. If my geometry knowledge is accurate, only squares and rhombi (is that the plural of "rhombus"?) are four-sided figures that have all 4 sides of equal length. Thus, when the Torah mentions that both length & width are the same, they could only be one of these two shapes. – DanF Feb 28 '19 at 19:35
  • You’re correct. What I mean is that if רבוע indicates a square, it doesn’t need to mention both the length and width; only one dimension is sufficient. From the fact that it mentions both dimensions indicates to me that a רבוע is a rectangle, only indicating that the sides intersect at right angles but saying nothing of their side lengths. The passuk then clarified that the lengths are the same. (A square is both a rhombus and a rectangle, all of which are parallelograms.) – DonielF Feb 28 '19 at 19:38
  • @DonielF You have a point, which puts to question as to exactly what רבוע means. It comes from the shoresh meaning "four". So, we know it's a 4 sided figure. The fact that it mentioned that the length and width are equal, would imply that it could be either a rhombus or a square. Thus, I inferred from the fact that the Torah included the word רבוע when it didn't need to means that רבוע means "square" to exclude that you could make these items rhomboid. Unless you consider an arc / sector not a "side"... – DanF Feb 28 '19 at 19:55