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Pterodactylus scolopaciceps Meyer, 1860 (Pterosauria, Pterodactyloidea) from the Upper Jurassic of Bavaria, Germany: The Problem of Cryptic Pterosaur Taxa in Early Ontogeny

Figure 5

A demonstration of i = tan−1a/b rescaling on triangles with opposing dimensions.

The plots at the top demonstrate the data distribution of the triangles illustrated below, where Q = raw quotient value of triangle length/depth, and i = rescaled quotient values of triangle length/depth. The colours of triangles Ai – Ci, Aii – Cii and D are replicated in the diamonds in the plots for clarity. The depths (di) of Ai – Ci are equal to the lengths (also di) of Aii – Cii respectively. Likewise, the lengths (dii) of Ai – Ci are equal to the depths (also dii) of Aii – Cii. D is an equilateral triangle, and on the plots it demonstrates the transition between tall and long forms. The diagram demonstrates that triangles with the same range of variation between both shallow-long forms and deep-short forms will only exhibit the true range of variation once the i = tan−1a/b rescaling has been applied.

Figure 5