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Glome in colors | R
What is the shape of the universe? Does it extend infinitely? We can go around the earth forever but can not find the end. Likewise, the universe may be finite and endless. Let's consider a mathematical model suitable for such a space.
http://qindex.info/d.php?c=5253#5309

Hollow Glome | R
A hollow glome can be a counterexample to the Poincaré conjecture. It is simply connected, closed 3-manifold but is not homeomorphic to the 3-sphere or glome.
http://qindex.info/d.php?c=5253#3558

04 Limits and Limit Laws in Calculus | R
Asymptote: a straight line approached by a given curve as one of the variables in the equation of the curve approaches infinity
http://qindex.info/d.php?c=5253#3456

06 Derivatives of Polynomial Functions | R
Power Rule, Product Rule, and Quotient Rule
http://qindex.info/d.php?c=5253#3455

2018-10-30 | R
2018-10-30 04:25
http://qindex.info/d.php?c=5253#3449

3-sphere | R
Any loop or circular path on the 3-sphere can be continuously shrunk to a point without leaving the 3-sphere. The Poincaré conjecture provides that the 3-sphere is the only three-dimensional manifold (up to homeomorphism) with these properties.
http://qindex.info/d.php?c=5253#3447

A Breakthrough in Higher Dimensional Spheres | R
Infinite Series | PBS Digital Studios
http://qindex.info/d.php?c=5253#5346

Basic Euclidian Geometry | R
In geometry, a point is a location in space. We can create a line by stringing an infinite number of points in a certain direction and vice verse.
http://qindex.info/d.php?c=5253#5247

Basic Euclidian Geometry | R
By stringing an infinite number of lines along a dimension perpendicular to the line, a two-dimensional object called a plane can be obtained. And then if we string an infinite number of planes in either direction, we get three dimensional space.
http://qindex.info/d.php?c=5253#5249

Closed set | R
A set which contains all its limit points. A closed set contains its own boundary.
http://qindex.info/d.php?c=5253#3476

Compact space | R
Compactness is a property that generalizes the notion of a subset of Euclidean space being closed (that is, containing all its limit points) and bounded(that is, having all its points lie within some fixed distance of each other). 
http://qindex.info/d.php?c=5253#3494

Connected space | R
A topological space X is said to be disconnected if it is the union of two disjoint nonempty open sets. Otherwise, X is said to be connected.
http://qindex.info/d.php?c=5253#3492

Derivatives of Trigonometric Functions | R
Derivatives of Trigonometric Functions
http://qindex.info/d.php?c=5253#3408

Dimensions | R
The number of dimensions is how many values are needed to locate points on a shape.
http://qindex.info/d.php?c=5253#3413

Dot Product Part 1 | R
Given two nonzero vectors in two or three dimensions, their dot product is the product of the magnitudes times the cosine of the angle between the two vectors.
http://qindex.info/d.php?c=5253#3411

Dot Product Part 2 | R
12.3 Dot Product Part 2
http://qindex.info/d.php?c=5253#3412

Figure 7 | R
12 straight paths passing through a point on a sphere are projected to the xy-plane.
http://qindex.info/d.php?c=5253#5370

Formulas for Trigonometric Functions | R
Sum/Difference, Double/Half-Angle, Prod-to-Sum/Sum-to-Prod
http://qindex.info/d.php?c=5253#3437

History of the Poincaré Conjecture | R
John Morgan
http://qindex.info/d.php?c=5253#5225

How Fast Is It - 01 - Preface | R
How Fast Is It - 01 - Preface (1080p)
http://qindex.info/d.php?c=5253#5360

How Fast Is It - 02 - The Speed of Light | R
How Fast Is It - 02 - The Speed of Light (1080p)
http://qindex.info/d.php?c=5253#5359

How Fast Is It - 03 - Special Relativity | R
How Fast Is It - 03 - Special Relativity (1080p)
http://qindex.info/d.php?c=5253#5358

How Fast Is It - 04 - General Relativity I - Geometry | R
How Fast Is It - 04 - General Relativity I - Geometry (1080p)
http://qindex.info/d.php?c=5253#5355

How the Universe Works | R
Blow your Mind of the Universe Part 11 - Space Discovery Documentary
http://qindex.info/d.php?c=5253#5380

Integration Using The Substitution Rule | R
To get the integral of the cosine of 2 times theta.
http://qindex.info/d.php?c=5253#3436

Leonard Susskind | R
The space itself may be more than three dimensions. But we can't visualize more dimensions. The architecture of the brain itself is evolved in the world of three dimensions. We only describe more dimensions by pure mathematics.
http://qindex.info/d.php?c=5253#5242

Loop | R
A loop in mathematics, in a topological space X is a continuous function f from the unit interval I = [0,1] to X such that f(0) = f(1).
http://qindex.info/d.php?c=5253#3450

n-ball | R
A set of points whose distance from a particular point is less than a specified length in n-dimensional space.
http://qindex.info/d.php?c=5253#3445

n-sphere | R
A set of points at a specified distance from a particular point in (n+1)-dimensional space. The pair of points at the ends of a line segment is a 0-sphere.
http://qindex.info/d.php?c=5253#3446

Non-Euclidean Geometry | R
Classroom Aid
http://qindex.info/d.php?c=5253#3389

Path | R
In mathematics, a path in a topological space X is a continuous function f from the unit interval I = [0,1] to X f : I → X. A topological space for which there exists a path connecting any two points is said to be path-connected. 
http://qindex.info/d.php?c=5253#3453

Real coordinate space | R
In mathematics, real coordinate space of n dimensions, written Rn (/ɑːrˈɛn/ ar-EN) (also written ℝn with blackboard bold) is a coordinate space that allows several (n) real variables to be treated as a single variable. 
http://qindex.info/d.php?c=5253#3495

Riemannian Curvature Tensor | R
Classroom Aid
http://qindex.info/d.php?c=5253#3394

Simply connected space | R
In topology, a topological space is called simply connected if it is path-connected and every path between two points can be continuously transformed into any other such path while preserving the two endpoints in question.
http://qindex.info/d.php?c=5253#3534

Singularities Explained | Infinite Series | R
Singularities Explained | Infinite Series
http://qindex.info/d.php?c=5253#3563

Space | R
A space consists of selected mathematical objects that are treated as points, and selected relationships between these points. 
http://qindex.info/d.php?c=5253#5251

The Poincare Conjecture | R
In the early 1900s mathematicians and physicists were very interested in the shape of space. New experiments and theories were being developed that would ultimately create relativity theory and change our entire view of the universe.
http://qindex.info/d.php?c=5253#3533

The Vector Dot Product | R
A dot B is equal to the length of A times the length of B times the cosine of the angle between them.
http://qindex.info/d.php?c=5253#3410

Thinking visually about higher dimensions | R
Thinking visually about higher dimensions
http://qindex.info/d.php?c=5253#3388

Tom Campbell | R
The assumption that space and time is continuous yields Zeno's paradox. The universe is not created out of continuous space and time.
http://qindex.info/d.php?c=5253#5024

Topological manifold | R
A topological space which locally resembles real n-dimensional space in a sense defined below.
http://qindex.info/d.php?c=5253#3493

volumes and surface areas of n-spheres  | R
Graphs of volumes and surface areas of n-spheres of radius 1.
http://qindex.info/d.php?c=5253#3448

Zeno's Paradox | R
To get to a point in the geometric space, you have to travel half way to that point and half way to that halfway point and so on. There's no end to the halfway so you can't reach the point.
http://qindex.info/d.php?c=5253#5248

Zeno's Paradox | 4
Defending Zeno's Paradox | R     Stochastic Supertasks | R     Supertasks | R     Zeno's Paradoxes | R    
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