gnomon

geometry

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June 29, 2026

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A gnomon is a device that indicates time through its shadow, often a vertical rod on a sundial. Historically, it also referred to a vertical line or a shape resembling a carpenter's square.12

In geometry, the term "gnomon" evolved. Early Greek mathematicians used it to describe figures added to existing shapes to create a larger, similar shape. For example, adding odd numbers (1, 3, 5, etc.) to a square number results in a larger square number, with the odd numbers themselves being called gnomons. Heron of Alexandria extended this concept to any figure that, when added to another, results in a similar whole. This geometric concept is linked to figurate numbers, such as triangular and pentagonal numbers.13

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gnomon
The term gnomon was at one time substantially synonymous with a vertical line. From this early use it came to represent a figure like a carpenter’s square but usually with equal arms. Seeking to relate numbers to geometric forms, early Greek mathematicians imagined squares as built up…
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The term gnomon was at one time substantially synonymous with a vertical line. From this early use it came to represent a figure like a carpenter’s square but usually with equal arms. Seeking to relate numbers to geometric forms, early Greek mathematicians imagined squares as built up…
Read More

number game
Polygonal and other figurate numbers
The gnomons include all of the odd numbers; these can be represented by a right angle, or a carpenter’s square, as illustrated in Figure 3. Gnomons were extremely useful to the Pythagoreans. They could build up squares by adding gnomons to smaller squares and from such…
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The gnomons include all of the odd numbers; these can be represented by a right angle, or a carpenter’s square, as illustrated in Figure 3. Gnomons were extremely useful to the Pythagoreans. They could build up squares by adding gnomons to smaller squares and from such…
Read More

Pythagoreanism
Arithmetic
…the early Pythagoreans used so-called gnōmones (“carpenter’s squares”). Judging from Aristotle’s account, gnomon numbers were represented by dots or pebbles arranged in a manner producing “square” and “oblong” shapes. If a series of odd numbers are put around the unit as gnomons, they always produce squares; thus, the members of…
Read More
…the early Pythagoreans used so-called gnōmones (“carpenter’s squares”). Judging from Aristotle’s account, gnomon numbers were represented by dots or pebbles arranged in a manner producing “square” and “oblong” shapes. If a series of odd numbers are put around the unit as gnomons, they always produce squares; thus, the members of…
Read More