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  2. Crystallographic restriction theorem - Wikipedia

    en.wikipedia.org/wiki/Crystallographic...

    Thus 5-fold rotational symmetry cannot be eliminated by an argument missing either of those assumptions. A Penrose tiling of the whole (infinite) plane can only have exact 5-fold rotational symmetry (of the whole tiling) about a single point, however, whereas the 4-fold and 6-fold lattices have infinitely many centres of rotational symmetry.

  3. Tripartite (theology) - Wikipedia

    en.wikipedia.org/wiki/Tripartite_(theology)

    The Old Testament consistently uses three primary words to describe the parts of man: basar (flesh), which refers to the external, material aspect of man (mostly in emphasizing human frailty); nephesh, which refers to the soul as well as the whole person or life; and ruach which is used to refer to the human spirit (ruach can mean "wind", "breath", or "spirit" depending on the context; cf ...

  4. Quasicrystal - Wikipedia

    en.wikipedia.org/wiki/Quasicrystal

    The more precise mathematical definition is that there is never translational symmetry in more than n – 1 linearly independent directions, where n is the dimension of the space filled, e.g., the three-dimensional tiling displayed in a quasicrystal may have translational symmetry in two directions.

  5. Penrose tiling - Wikipedia

    en.wikipedia.org/wiki/Penrose_tiling

    The pattern represented by every finite patch of tiles in a Penrose tiling occurs infinitely many times throughout the tiling. They are quasicrystals: implemented as a physical structure a Penrose tiling will produce diffraction patterns with Bragg peaks and five-fold symmetry, revealing the repeated patterns and fixed orientations of its tiles ...

  6. Alan Lindsay Mackay - Wikipedia

    en.wikipedia.org/wiki/Alan_Lindsay_Mackay

    He is a pioneer in the introduction of five-fold symmetry in materials and in 1981 predicted quasicrystals in a paper (in Russian) entitled "De Nive Quinquangula" [3] in which he used a Penrose tiling in two and three dimensions to predict a new kind of ordered structures not allowed by traditional crystallography.

  7. Pardes (exegesis) - Wikipedia

    en.wikipedia.org/wiki/Pardes_(exegesis)

    Each type of Pardes interpretation examines the extended meaning of a text. As a general rule, the extended meaning never contradicts the base meaning. [8] The Peshat means the plain or contextual meaning of the text. Remez is the allegorical meaning. Derash includes the metaphorical meaning, and Sod represents the hidden meaning. There is ...

  8. The two kinds of righteousness - Wikipedia

    en.wikipedia.org/wiki/The_two_kinds_of_righteousness

    The two kinds of righteousness is a Lutheran paradigm (like the two kingdoms doctrine).It attempts to define man's identity in relation to God and to the rest of creation. The two kinds of righteousness is explicitly mentioned in Luther's 1518 sermon entitled "Two Kinds of Righteousness", in Luther's Commentary on the Epistle to the Galatians (1535), in his On the Bondage of the Will ...

  9. Girih - Wikipedia

    en.wikipedia.org/wiki/Girih

    A periodic tiling of the plane is the regular repetition of a "unit cell", in the manner of a wallpaper, without any gaps. Such tilings can be seen as a two-dimensional crystal, and because of the crystallographic restriction theorem, the unit cell is restricted to a rotational symmetry of 2-fold, 3-fold, 4-fold, and 6-fold. It is therefore ...

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