For the curve , r = ( 2abt, a^2 log t, b^2t^2 ), Show that k = - T = 2abt/(a^2 + 2b^2 + t^2)^2 where k = curvature of the curve, T = torsion of the curve

Differential Geometry (II) Curves in Space Curvature of the Curve Torsion of the Curve For the curve r = ( 2abt, a^2 log t, b^2t^2 ) Show that k = - T = 2abt/(a^2 + 2b^2 + t^2)^2 where k = curvature of the curve T = torsion of th ...continues

For the curve r = ( √6 at^3, a(1+3t^2), √6 at ), Show that k = - T = 1/[a(3t^2 + 1)^2] where k = curvature of the curve, T = torsion of the curve.

Differential Geometry (I) Curves in Space Curvature of the Curve Torsion of the Curve For the curve r = ( √6 at^3, a(1+3t^2), √6 at ) Show that k = - T = 1/[a(3t^2 + 1)^2] where k = curvature of the curve, T = tors ...continues

Proof Incircle

Let r be the radius on the incircle of tri ABC and a,b,c be the radii of the excircles opposite vertices A, B, and C, respectively. Ilustrate the fact that 1/r = 1/a + 1/b + 1/c. Also, write a proof of this.

Proof Involving Isoceles Triangle

Prove: The two segments joining the vertex of an isosceles triangle with the trisected points of the base are congruent.

Circumscribable Quadrilateral and Finding Lengths

In the attached figure, the quadrilateral ABCD has the following lengths of sides and diagonals: DC=7, CB=8, BA=13, AD=13, AC=15, and BD=13. 1. Verify that quadrilateral ABCD is circumscribable 2. Find the remaining lengths of DE, BE, AE, and CE. Although it appears there is a right angle, it is not labeled as though it ...continues

Construct a geometric model using axioms

Construct a model that satisfies the following axioms. - 1. There exists at least 1 line. - 2. Every line of the geometry has exactly 4 points on it. - 3. Not all points of the geometry are on the same line. - 4. Each point of the geometry is contained in exactly 3 lines. - 5. Every pair of lines intersect and their interse ...continues

Poincare Half Plane and H-line

Given points A(2,5) and B(6,3) in the Poincare half plane where the axis is the line that determines the half plane - A. Find the equation of the h-line that passes through A and B - B. Find AB* using the definition of distance shown in the attachment: AB* = absolute value (ln(AM x BN)/(BM x AN))) - C. Find 2 points C and ...continues

Geometric constructions

USING ONLY AN UNMARKED STRAIGHT EDGE AND A COMPASS CONSTRUCT THE FOLLOWING: (A) A RHOMBUS GIVEN: ONE SIDE AND ONE ANGLE (B) A PARALLELOGRAM GIVEN: TWO ADJACENT SIDES AND THE INCLUDED ANGLE (C) A PARALELLOGRAM GIVEN: THE DIAGONALS AND THE ANGLE BETWEEN THEM ********I NEED STEP-BY-STEP INSTRUCTIONS ON HOW TO CONSTRUCT ...continues

Centroid-Balance Point of a Triangle Proof

Need to prove that centroid of a triangular region is the balance point. The trick is that I can't use the "equal areas" argument.

Point of Minimal Distance : Equilateral Triangle

Using GEOMETRY ONLY, for an equilateral triangular region, for which points is the sum of the distances to the sides of the triangle minimal? Please show me and do not point to a web site.