Authors: Alexander Egoyan
Comments: 6 pages.
In this work a new approach to multidimensional geometry based on smooth infinitesimal analysis (SIA) is
proposed. An embedded surface in this multidimensional geometry will look different for the external and internal
observers: from the outside it will look like a composition of infinitesimal segments, while from the inside like a set of
points equipped by a metric. The geometry is elastic. Embedded surfaces possess dual metric: internal and external.
They can change their form in the bulk without changing the internal metric.