diagonal

Everyday

1. (adjective) Diagonal means going in a slanting line, not straight across or straight up. tree →
2. (maths, noun) A diagonal is a straight line that joins two corners of a shape that are not next to each other. tree →
3. (adverb) Diagonally means in a slanting direction, from one corner towards the opposite one. tree →

In the lessons

A key geometry word: a square and a rectangle each have 2 diagonals, a pentagon has 5, a triangle has none. In everyday life you cut sandwiches diagonally or cross a field diagonally. In chess the bishop moves diagonally. Phrases: diagonal line, draw the diagonal, diagonally opposite.

Examples

• Draw a diagonal from one corner of the square to the opposite corner. tree →
• A rectangle has two diagonals. tree →
• Mum cut my toast diagonally into triangles. tree →
• The bishop moves diagonally across the chessboard. tree →
• Our house is diagonally opposite the shop. tree →
• The diagonal stripes on his tie were red and blue. tree →
• A triangle has no diagonals. tree →

Note

In maths: the two diagonals of a square are equal and cross at right angles; a diagonal cuts a square or rectangle into two equal triangles; a polygon with n sides has n × (n − 3) ÷ 2 diagonals (hexagon: 6 × 3 ÷ 2 = 9). Sides are not diagonals.

In Jewish tradition

In Sefer Yetzirah, the twelve diagonal borders are the twelve edges of a cube-like space, which stand for the twelve simple letters.

Interpretation. Tradition reads these edges as marking out the six directions, and the world, with their boundaries extending without end.

Examples

• == Chapter 6 == [6:1] Three Fathers and their descendants, and Seven Stars [another version: Conquerors] and their hosts, and Twelve Diagonal Borders. (Sefer Yetzirah, Sefaria community translation) tree →
• Their measure is the Twelve Diagonal Borders: Northeastern border, Southeastern border, Upper-Eastern border, Lower-Western border, Upper-Northern border, Lower-Northern border, Southwestern border, Northwestern border, Upper-Western border, Lower-Western border, Upper-Southern border, Lower-Southern border. (Sefer Yetzirah, Sefaria community translation) tree →

Note

In maths: the two diagonals of a square are equal and cross at right angles; a diagonal cuts a square or rectangle into two equal triangles; a polygon with n sides has n × (n − 3) ÷ 2 diagonals (hexagon: 6 × 3 ÷ 2 = 9). Sides are not diagonals.