Could someone try to explain what a Manifold is to me? I've tried to, but haven't been able to find a consistent set of qualities that I could really make a definition into.
Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
In essence it means "many". What context are you using it in?
espex u r right
Definition: A cylindrical pipe fitting, having a number of lateral outlets, for connecting one pipe with several others.
Definition: The third stomach of a ruminant animal.
Definition: To take copies of by the process of manifold writing; as, to manifold a letter.
Definition: a pipe that has several lateral outlets to or from other pipes
Definition: a set of points such as those of a closed surface or and analogue in three or more dimensions
Definition: a lightweight paper used with carbon paper to make multiple copies; "an original and two manifolds"
Definition: combine or increase by multiplication; "He managed to multiply his profits"
Definition: make multiple copies of; "multiply a letter"
Definition: many and varied; having many features or forms; "manifold reasons"; "our manifold failings"; "manifold intelligence"; "the multiplex opportunities in high technology"
Not the answer you are looking for? Search for more explanations.
In basic language it refers to a surface of arbitrary dimension that can be treated as flat over a very small distance. An example is the earth. It seems flat because you're really close but in reality its curved. A more rigorous definition is that it is a continuously differentiable region, which employs a differential metric, that is space must be measured in small units in order for the rules of calculus to work. A local set of coordinates can be set up at any point and "regular" euclidian geometry can be applied there. For example all smooth continuous curves are manifolds. For example the parabola: it looks curved but in the limit of two points coming together along it you'll eventually have a straight line, which is the derivative (or slope) at that point. Their analysis uses a more abstract entity called a tensor. Think of these as generalized vectors, to higher dimensions. This is a complicated field of math but I hope my simplified description helps.