Mobius Engagement Ring in with diamond 0.21 & 0.20ct in 18k White Gold

In mathematics, a Möbius strip, band, or loop, also spelt Mobius or Moebius, is a surface with only one side (when embedded in three-dimensional Euclidean space) and only one boundary curve. The Möbius strip is the simplest non-orientable surface. It can be realized as a ruled surface. Its discovery is attributed independently to the German mathematicians Johann Benedict Listing and August Ferdinand Möbius in 1858, though similar structures can be seen in Roman mosaics c. 200–250 AD. Möbius published his results in his articles "Theorie der elementaren Verwandtschaft" (1863) and "Ueber die Bestimmung des Inhaltes eines Polyëders" (1865).

An example of a Möbius strip can be made by taking a strip of paper and giving one end a half-twist, then joining the ends to form a loop; its boundary is a simple closed curve which can be traced by a single unknotted string. Any topological space homeomorphic to this example is also called a Möbius strip, allowing for a very wide variety of geometric realizations as surfaces with a definite size and shape. For example, any rectangle can be glued left-edge to right-edge with a reversal of orientation. Some, but not all, of these can be smoothly modelled as surfaces in Euclidean space. A closely related, but not homeomorphic, the surface is the complete open Möbius band, a surface with no boundaries in which the width of the strip is extended infinitely to become a Euclidean line.

A half-twist clockwise gives an embedding of the Möbius strip which cannot be moved or stretched to give the half-twist counterclockwise; thus, a Möbius strip embedded in Euclidean space is a chiral object with right- or left-handedness. The Möbius strip can also be embedded by twisting the strip any odd number of times, or by knotting and twisting the strip before joining its ends.

Finding algebraic equations cutting out a Möbius strip is straightforward, but these equations do not describe the same geometric shape as the twisted paper model above. Such paper models are developable surfaces having zero Gaussian curvature and can be described by differential-algebraic equations.

• Metal: 18K White Gold
• Gemstones: Diamond
• Style of cut: Round Brilliant Cut
• Colour: H (White)
• Clarity: VS2 (Very Slightly Included 2)
• Carat weight: 0.21ct & 0.20ct
• Quality of cut: Very Good
• Weight: 3.80gr
• Guarantee: Makriadis Jewelry