The Shape of the M in the MO-Labs-Logo

The shape of the M in the MO-Labs-Logo is quite special and closely related to the subject of this blog. It belongs to a surface with a so-called cusp singularity, sometimes also called A4-singularity.

Singularities of surfaces are very special points. In most parts of a surface, the shape looks quite smooth, but in some it might not; such points are likely to be singularities.

The particular shape of the surface depicted in our logo is determined by the equation x2-y2=z5. Actually, the logo only shows its silhouette which is essentially the intersection of the surface with the plane y=0, namely the plane curve x2=z5 in the z/x-plane (or when replacing z by y in the y/x-plane):

The MO-Labs-Logo-M-Curve.
The MO-Labs-Logo-M-Curve.

 

The related Math Objects in our sculpture shop are:

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Some related links to external websites: