What is curvature perturbations?
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"What are curvature perturbations?"\n"What is curvature perturbation?"\n\nYou don't define your terms very well.\n\nCurvature - do you mean space time curvature tensor?\nPerturbation is a disturbance, but is sometimes meant as the event or as the cause of the event.\n\nSo is curvature perturbing something or is something perturbing curvature?
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Your dad was right: space-time curvature is not something you can really understand outside from the mathematics framework of general relativity.\nHowever, the concept of the space bending can be intuitively pictured by a simple thought experiment: imagine we lived in a 2-dimensional world, that is, on a flat surface. This means we live completely within the surface, never escaping from it, maybe not even knowing that there are other dimensions. Then suppose this surface is bent due to some effect (gravity, in our case). If the bending is strong enough (if there is enough mass in the universe), the surface may be so curved to close on itself, for example forming a sphere.\nIn this imaginary scenario, you may build a spaceship and travel in a straight line from your viewpoint. But remember, you are traveling within the sphere surface. Seen from a 3D observer, your straight line is a circle. Therefore, in the end you will get at the starting point of the circle.
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Smooth surfaces\nLubricants\nRoller and Bowler baring
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isthegeometricaltheoryofgravitationwhichunifiesspecialrelativityandIsaacNewton'slawof universalgravitationwiththeinsightthatgravitationisnotduetoa forcebutratherisamanifestationofcurvedspaceandtimethis curvaturebeingproducedbythemass-energyand momentumcontentofthe spacetime
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hmmm taking me way back here.  when you break the area under a curve into rectangles of differential width,  either the left top corner will lie on the curve or the right top corner will.  \n\nas you decrease the differential width the area will become more exact until bada bing you are doing calculus.  i think.
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something to do with the curved space-time continuum
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Most introductory books on differential geometry discuss this. Looks at 'From Calculus to Cohomology' and 'Introduction to Smooth Manifolds' as references.
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Ellipse is for positive curvature and hyperbola for negative curvature.
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In Peyronie's disease, anomalous scar tissue grows in the soft tissue of the penis, causing curvature. Severe cases can benefit from surgical correction.\n\nMost curves are natural, but if it's severe it could be this Peyronie's Disease...  I'd see a doctor if it's a severe curvature.
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c causes the graph to shift right (if c <0) ir left (if c>0),\n\nd causes it to shift up (if d>0) or down (if d < 0)
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Spiral, lenticular, elliptical and irregular\n\nSee the link
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Hi. It is bent at any height above zero. Look at the horizon from a spacecraft and you'll see this. The bending gets reduced as you approach zero height, at which point it is a flat circle.
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Graph against what?\ni'm assuming against position and constant increase of accelaration. \nThe graph looks same as constant accelaration (parabola) but with steeper curve. \nTry to ploy y=x^3. This will be the graph.
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Yes.\ngravity is inversely proportional to radius squared, and radius is inversely proportional to the curvature of the same surface, so your statement is true.
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Differential geometry/manifolds, Optimization word problems in 3D, topology proofs.
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Any object that appears to be forced by gravity can be used as an example.  A baseball appears to move in an arc.  It, however is moving in a straight line.  The gravity of the earth bends the space that that straight line is in, causing it to appear curved.
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Bernoulli Effects\n\nSee how to demonstrate it here --> http://www.physics.umn.edu/outreach/pforce/Bernoulli.html