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Every odd perfect square is a centered octagonal number. The difference between any two odd perfect squares is a multiple of 8. The difference between 1 and any higher odd perfect square always is eight times a triangular number, while the difference between 9 and any higher odd perfect square is eight times a triangular number minus eight.
Leaves of most plants include a flat structure called the blade or lamina supported by a network of veins, a petiole and a leaf base; [1] but not all leaves are flat, some are cylindrical. [ citation needed ] Leaves may be simple, with a single leaf blade, or compound, with several leaflets .
Living sculpture is any type of sculpture that is created with living, growing grasses, vines, plants or trees.It can be functional and/or ornamental. There are several different types of living sculpture techniques, including topiary (prune plants or train them over frames), sod works (create sculptures using soil and grass or moss), tree shaping (growing designs with living trees) and mowing ...
Part of the soft systems methodology, rich pictures provide a mechanism for learning about complex or ill-defined problems by drawing detailed ("rich") representations of them. [1] Typically, rich pictures follow no commonly agreed syntax , usually consist of symbols , cartoons , sketches or doodles and can contain as much (pictorial ...
All square triangular numbers have the form , where is a convergent to the continued fraction expansion of , the square root of 2. [ 4 ] A. V. Sylwester gave a short proof that there are infinitely many square triangular numbers: If the n {\displaystyle n} th triangular number n ( n + 1 ) 2 {\displaystyle {\tfrac {n(n+1)}{2}}} is square, then ...
Fractal fern in four states of construction. Highlighted triangles show how the half of one leaflet is transformed to half of one whole leaf or frond.. Though Barnsley's fern could in theory be plotted by hand with a pen and graph paper, the number of iterations necessary runs into the tens of thousands, which makes use of a computer practically mandatory.
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Variation in leaves from the giant ragweed illustrating positional effects. The lobed leaves come from the base of the plant, while the unlobed leaves come from the top of the plant. Although plants produce numerous copies of the same organ during their lives, not all copies of a particular organ will be identical.