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The Monge gauge has two obvious limitations: If the average surface is not plane, then the Monge gauge only makes sense on length scales smaller than the curvature of the average surface. And the Monge gauge fails completely if the surface is so strongly bent that there are overhangs (points x,y corresponding to more than one z ).
The vertebral column, also known as the spinal column, spine or backbone, is the core part of the axial skeleton in vertebrate animals.The vertebral column is the defining and eponymous characteristic of the vertebrate endoskeleton, where the notochord (an elastic collagen-wrapped glycoprotein rod) found in all chordates has been replaced by a segmented series of mineralized irregular bones ...
The now obsolete Harrington rod operated on a ratchet system, attached by hooks to the spine at the top and bottom of the curvature that when cranked would distract—or straighten—the curve. The Harrington rod obviates the need for prolonged casting, allowing patients greater mobility in the postoperative period and significantly reducing ...
Curvature of general surfaces was first studied by Euler. In 1760 [4] he proved a formula for the curvature of a plane section of a surface and in 1771 [5] he considered surfaces represented in a parametric form. Monge laid down the foundations of their theory in his classical memoir L'application de l'analyse à la géometrie which
The number of vertebrae in a region can vary but overall the number remains the same. In a human spinal column, there are normally 33 vertebrae. [3] The upper 24 pre-sacral vertebrae are articulating and separated from each other by intervertebral discs, and the lower nine are fused in adults, five in the sacrum and four in the coccyx, or tailbone.
Lordosis is historically defined as an abnormal inward curvature of the lumbar spine. [1] [2] However, the terms lordosis and lordotic are also used to refer to the normal inward curvature of the lumbar and cervical regions of the human spine. [3] [4] Similarly, kyphosis historically refers to abnormal convex curvature of the spine
Kyphoscoliosis describes an abnormal curvature of the spine in both the coronal and sagittal planes. It is a combination of kyphosis and scoliosis.This musculoskeletal disorder often leads to other issues in patients, such as under-ventilation of lungs, pulmonary hypertension, difficulty in performing day-to-day activities, and psychological issues emanating from anxiety about acceptance among ...
Any surface with an isolated umbilic point at the origin can be expressed as a Monge form parameterisation = (+) + (+ + +) + …, where is the unique principal curvature. The type of umbilic is classified by the cubic form from the cubic part and corresponding Jacobian cubic form.
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