39 ZSOLT LÁNGI_ AN ISOPERIMETRIC PROBLEM FOR THREE-DIMENSIONAL PARALLELOHEDRA 1:04:27 MOTIVATION AND ALGEBRAIC BACKGROUND - LECTURE 1 1:07:10 PERFECT MATCHINGS IN GRAPHINGS 1:25:31 THE FRACTAL (MANDELBROT) PERCOLATION IS UNRECTIFIABLE 1:13:36 THE MANY FACETS OF HIGGS BUNDLES 1:07:19 ...
Explain the possible relationships between two lines in R^3. Lines g and h are parallel and m\angle 1= 65^\circ. What is m\angle 7? For what value of x will make a parallel to b? Name the lines (if any) that must be parallel under the given condition. l \perp p ...
What is an interior point in real analysis? What is the validity coefficient? What does the divergence measure? For what value of x will make a parallel to b? What are the steps in verifying that -ln|secx+tanx| = ln|secx-tanx| ...
Which of these axioms is analogous to Playfair's Postulate? How is this axiom different from Euclid's parallel postulate? Is the Euclidean plane finite, or infinite? Does the Euclidean plane satisfy the affine axioms? Define inductive reasonin...
By Bertrand’s postulate, there is always at least one prime between x and 2x; by testing each one of these integers in turn for primality, one can thus obtain a deterministic algorithm to find primes in time . But one should be able to do much better. For comparison, if probabilistic ...
pair postulate, we can label every pair of corresponding angles as either α or β. Since for every pair of angles α and β, the sum is 180°, and thealternate interior anglesare equal. Thus, by the converse of the same side interior angle theorem, line P and line Q are parallel. ...
Basic physics states that if there are no external forces at work, an object will always travel in the straightest possible line. Accordingly, without an external force, two objects traveling along parallel paths will always remain parallel. They will never meet. But the fact is, they do meet...
While they are non-commutative, they do keep many other properties of the complex numbers: Being non-commutative, the quaternions do not form a field. However, they are still a skew field (or division ring): multiplication is associative, and every non-zero quaternion has a unique ...
What is a relation in general mathematics? What is the duality theorem? Define common difference What is Demorgan's theorem? What is the equipartition theorem? Which of the following four lines are parallel?Are any of them identical? L_1: x = 1 + 6t, y = 1 - 3t, z = 12t + 5,...
Two lines within a plane are said to be parallel if they never meet. This means that even if extended out infinitely the two lines will never cross each other at any point. If two parallel lines are both intersected by a third transversal line in such a way that there is an angle of...