To judge whether a spiral is an equiangular spiral,‭ ‬certain measurements are made and then these values are placed into the established formulas.  Following this,‭ ‬a model can be made using the data and if an equiangular model is produced,‭ ‬then it is valid.  From what is known of the organism and its growth,‭ ‬the growth and consequent spiral is that of equiangular.

Using Mathematica,‭ ‬it is possible to get the plot coordinates of an image.  The image was copied into a Mathematica notebook and the using the‭ “‬Get Coordinates‭” ‬feature,‭ ‬a series of polar coordinates were taken from the line.  This process is manual and requires the use of the left mouse button and the‭ “‬Control‭” ‬keyboard button.  Once these points were plotted,‭ ‬using Mathematica,‭ ‬these values were taken from the program’s memory and‭ “‬copied as‭” ‬MATHML formatted data.  Once in this format,‭ ‬the points were‭ “‬pasted as‭” ‬into a notebook as formatted text.

Once the points were in the notebook,‭ ‬the following steps were taken to prepare the data so that the curve could be re-constructed,‭ ‬and its formula,‭ ‬coefficients and least squares of the line be generated.

Cerioshell may be used to quantitatively model patterns of ontogenesis and cladogenesis in‭ ‬Prunum.

Our modeling is being used to determine possible constraints or limiting features have influenced the constructional morphology of‭ ‬Prunum‭ (‬i.e. functional/adaptational,‭ ‬fabricational/morphogenetic,‭ ‬and/or historical/phylogenetic‭)‬.

When reviewing the pattern of frequency distribution,‭ ‬often it appears as if the distribution changed positions within the theoretical morphospace from geological period to period.  However,‭ ‬it appears that when extinctions occur,‭ ‬and new organisms evolve,‭ ‬there is simply a repeating of the same morphologic themes in terms of proportions.  Why is this?

Is it possible to take a shell and its mathematical function that represents it,‭ ‬modify certain parameters‭ (‬i.e. translation‭ – ‬the abapical migration,‭ ‬offset‭ & ‬its effect on radial migration,‭ ‬and the changes in horizontal and vertical dimensions of the aperture,‭ ‬and model shells of different species‭?‬

How accurately do mathematical models represent the actual ontogenetic processes that generate patterns of skeletogenesis‭?‬

From the time that Richard Feynman gave a talk on December‭ ‬29th‭ ‬1959‭ ‬at the annual meeting of the‭ ‬American Physical Society at the California Institute of Technology‭ (‬Caltech‭)‬ – There’s Plenty of Room at the Bottom,‭ ‬people have been fascinated by Feynman’s‭ “‬problem of manipulating and controlling things on a small scale.‭”‬

Currently,‎ ‏this small-scale manipulation is referred to as nanotechnology.  According to the definition provided by NASA,‭ “‬Nanotechnology is the creation of functional materials,‭ ‬devices and systems through control of matter on the nanometer length scale‭ (‬1-100‭ ‬nanometers‭)‬,‭ ‬and exploitation of novel phenomena and properties‭ (‬physical,‭ ‬chemical,‭ ‬biological,‭ ‬mechanical,‭ ‬electrical...‭) ‬at that length scale.‭” ‬

To put this concept into perspective,‎ ‏it is important to note that a human blood cell measures approximately‭ ‬2,000‭ ‬nm,‭ ‬well beyond the realm of nanotechnology.