What is "pinch point"

n. 1 (context engineering English) A point in between moving and stationary parts of a machine where an individual's body part may become caught, leading to injuryAmerican Short Line & Regional Railroad Association (n.d.) . 2 (context economics English) The level of inventories of a commodity or product below which consumers become concerned about security of supply 3 (context mathematics English) Cuspidal point, a type of singular point on an algebraic surface 4 A kerb extension, a traffic calming measure consisting of an angled narrowing of the roadway 5 A bottleneck, part of a process that is too slow and causes a delay

A pinch-point is the level of inventories of a commodity or product below which consumers of that commodity or product become concerned about security of supply. When inventories are below the pinch-point, small changes in the balance of supply and demand can cause large changes in the price of the commodity or product.

The term was suggested in 1988 by Walter Curlook (Executive Vice-President of Inco Ltd) and was first published by Raymond Goldie with Rob Maiman in 1990. In 2000 Raymond Goldie trademarked the term.

Pinch point may refer to:

• Pinch point (economics), the level of inventories of a commodity or product below which consumers become concerned about security of supply
• Pinch point (mathematics), a type of singular point on an algebraic surface
• Pinch point bar, a hand tool consisting of a long, straight metal bar
• Kerb extension, a traffic calming measure consisting of an angled narrowing of the roadway
• The point of closest approach between the hot and cold composite curves in pinch analysis

right|frame|240px|Section of the Whitney umbrella, an example of pinch point singularity. In geometry, a pinch point or cuspidal point is a type of singular point on an algebraic surface.

The equation for the surface near a pinch point may be put in the form

f(u, v, w) = u − vw + [4] 

where [4] denotes terms of degree 4 or more and v is not a square in the ring of functions.

For example the surface 1 − 2x + x − yz = 0 near the point (1, 0, 0), meaning in coordinates vanishing at that point, has the form above. In fact, if u = 1 − x, v = y and w = z then {u, v, w} is a system of coordinates vanishing at (1, 0, 0) then 1 − 2x + x − yz = (1 − x) − yz = u − vw is written in the canonical form.

The simplest example of a pinch point is the hypersurface defined by the equation u − vw = 0 called Whitney umbrella.

The pinch point (in this case the origin) is a limit of normal crossings singular points (the v-axis in this case). These singular points are intimately related in the sense that in order to resolve the pinch point singularity one must blow-up the whole v-axis and not only the pinch point.