Review Vocabulary

Allometric growth A pattern of growth in which the length of one feature grows at a rate proportional to a power of the length of another feature. (pp. p. 762 p. 763)

Area scaling factor The ratio of the area of any part of one figure to the corresponding part of another, equal to the square of the linear scaling factor. (p. 739)

Area-volume tension A result of the fact that as an object is scaled up, the volume increases faster than the surface area and faster than areas of cross sections. (p. 755)

Base-10 logarithmic scale A scale on which equal divisions correspond to powers of 10. (p. 762)

Crushing strength The maximum ability of a substance to withstand pressure without being crushed or deformed. (p. 750)

Density Mass per unit volume. (p. 747)

Geometric similarity Two objects are geometrically similar if they have the same shape, regardless of the materials of which they are made. They need not be the same size. Corresponding linear dimensions must have the same factor of proportionality. (p. 738)

Isometric growth Proportional growth. (p. 762)

Linear (length) scaling factor The number by which each linear dimension of an object is multiplied when it is scaled up or down; that is, the ratio of the length of any part of one of two geometrically similar objects to the length of the corresponding part of the second. (p. 738)

Log-log paper Graph paper on which both the vertical and the horizontal scales are logarithmic scales; that is, the scales are marked in orders of magnitude 1, 10, 100, 1000, …, instead of 1, 2, 3, 4, …. (p. 762)

Orders of magnitude Powers of 10. (p. 762)

Power curve A curve described by an equation , so that is proportional to a power of . (p. 764)

Pressure Force per unit area. (p. 747)

Problem of scale As an object or being is scaled up, its surface and cross-sectional areas increase at a rate different from its volume, forcing adaptations of materials or shape. (p. 754)

Proportional growth Growth according to geometric similarity, where the length of every part of the organism enlarges by the same linear scaling factor. (p. 760)

Semilog paper Graph paper on which only one of the scales is a logarithmic scale. (p. 762)

Volume scaling factor The ratio of a volume of any part of one figure to the corresponding part of another, equal to the cube of the linear scaling factor. (p. 740)

Weight Attractive force of a mass toward the center of the Earth, as measured at sea level. (p. 747)

Wing loading Weight supported divided by wing area. (p. 756)