Cancer: Uncontrolled growth of tissue resulting from the continuous and rapid production and reproduction of abnormal cells that invade and destroy other tissues.
When cancer cells were discovered they were named after the Greek word for crab because when viewed microscopically they appear crab-like or star-like.
Certain cell structures are considered cancerous more often than others. These are crab-like, star-like, in structure. Most notably, in breast X-rays, noncancerous tumors will tend to appear round (spherical) while cancerous ones will look more star-like. This is not to say that all star-like cells are cancerous but rather all cancerous cells appear star-like.
Specialists are very adept at detecting cancerous cells with the advanced technology and imaging equipment available today. However there is a very practical mathematical procedure that can identify whether the image of a cell structure requires a more thorough examination to determine whether it is cancerous or not.
A mathemtical calculation can determine a common feature of cancerous cells. This has to do with compactness of the cell structure. If the cell structure is relatively compact it is not considered cancerous while a cell cluster that is undifferentiated (or not compact) is scrutinized a bit closer for cancerous tendencies. This mathematical calculation is based on a ratio of perimeter (p) and area (a) of the 2-D image of the cell.
Calculation: We will call this ratio, r where r = p^2/a. Or, the ratio of perimeter-squared to area. This is as Bacus & Grose described, the Nuclear Shape of the cell as a classification of cancerous cell features.