A pipe is supported by a block and a wall. Find the pipe radius in term of the block height and its distance from the wall.

A block with height "b" is placed a distance "a" from a wall, to hold in place a pipe with radius "R" (The pipe is supported by the wall on the other side - see attached figure). Find the radius "R" in terms of "a" and "b".

Creating the formula to find the dimensions of a cube.

In Metric. Three college students are trapped in deep snow in northern Canada. To survive they must build an igloo using snow large enough for all of them to fit and small enough to not exceed their strength and stamina. Luckily one of them is a math major and quickly formulates the dimensions of the blocks they need to cu ...continues

For the curve , r = ( 2abt, a^2 log t, b^2t^2 ), Show that κ = - τ = 2abt/(a^2 + 2b^2t^2)^2 where κ = curvature of the curve, τ = 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: κ = - τ = 2abt/(a^2 + 2b^2t^2)^2 where κ = curvature of the curve ...continues

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

Distance travelled around box problem

An ant is walking around the outside of the cube in "straight" paths (where we define a straight path in this case as one formed by the edges of a cross section created by a plane slicing through the cube). For example, to get from point Q to point R in the picture above on the right, the ant walks along the red path. There are ...continues

An elegant proof of pythagoras' theorem

Prove Pythagoras' theorem.

Geometer's Sketchpad

Given triangle ABC with no angle >120 degrees, find and construct the point P for which PA + PB + PC is a minimum. What is this point called? What would be the case for a triangle with an angle of 120 degrees or more? ------------------------------------------------------ I need this done in Geometer's sketchpad as well as st ...continues

Heron's Formula

How is Heron's Formula used for finding the area of a triangle?

Pythagorean Theorem

I need to use the theorem to show that the area on the outside of A plus the outside of B = outside of C. I can't use something as easy as a square but I don't need anything too crazy. Please help with any suggestions as well as how I would find the area.

Transformation Geometry Proofs : Reflections

Please see the attached file for the fully formatted problems. Let l, m, n be distinct lines and P, Q, R be distinct points. Prove the following: (a) sigma l sigma m = sigma m sigma l if and only if l perpendicular to m. (b) sigma p sigma m = sigma m sigma p if and only if P E m. plus three more questions