Recent content by deRoy

Ok, let's see.. 1) I would start with rung 1 first, for if the first bottle breaks it's just 1 trial. If not then I would move to rung 51. 2) If the first bottle doesn't break, I would move to rung 52 for if it breaks as in case 1) it's just two trials so far. If not then move 100-52 = 48/2 =...

I think it has to do with CO2. CO2 dissolves in water, at low temperature and high pressures. When you closed the lid you pressurized the air. Then if the temperature rose a little, or if the jug was contaminated with impurities, or if a big truck passing outside shook the building, air...

Foie gras is made from the grotesquely enlarged livers of ducks and geese who have been cruelly force-fed.

Oh, I guess there will be many apartments on the 75th floor and above in Miami or Hong Kong say, complete with balconies to lounge outside. I wish I were living in one but no! I am just asking what's the situation with all this traffic and city noise below your feet.

What is the noise level at a high rise building if one was supposed to leave the window open in a balcony on the 80-th floor and above in an apartment on a skyscraper built in the city center of a large city like New York or Seoul, with all this car traffic underneath with their horns and sirens...

Ok, having constructed the line segment representing the area of the triangle, now also construct its square root line segment with ruler and compass. Now draw the square with that side and you have a square with area your triangle's area. The square with area given by the Heron's formula...

Do you know how to construct the product of two numbers with ruler and compass? By taking a line segment of length a and another of length b, do you know how to construct a line segment of length ab? s=(a+b+c)/2 is easily constructible with ruler and compass. And so is the formula given by...

Here, I have found a reference in Spivak's book: The metric, is determined if Q(W) ( Gaussian Curvature ) is known for n(n-1)/2 independent 2-dimensional subspaces at each point q. Michael Spivak: "A comprehensive Introduction to Differential Geometry" Vol. 2 page 179 I wish I had the time to...

What I am concluding is that sectional curvature defines the curvature tensor completely. And so does Riemann when he says that there are n(n-1)/2 functions that define the metric ( hence the curvature ) completely. Each differential equation is just the sectional curvature given by Gauss in his...

Riemann's lecture: " On the hypotheses which lie...". Haven't done it by hand yet, but it shouldn't pose any problem to find the Gaussian Curvature of any 2-plane of a hypersurface. And without tensors involved...

I think you mean that 20 numbers define the Riemann curvature tensor of a 4-hypersurface. My point was that for an n-hypersurface there are n(n-1)/2 numbers that define its intrinsic Curvature completely, namely the Gaussian Curvatures of n(n-1)/2 sectional 2-planes through a point. And of...

Why so? I was thinking up to now, that for any 4-dimensional manifold in x,y,z,t coordinates say, the Riemann tensor was just an elegant formula prescription way to calculate the Gaussian curvature at a point in 6 distinct planar sections of space-time, namely at the xy, xz, xt, yz, yt, zt...

But do you backup the backups? Because you are in great danger, otherwise!

A is a function of s of a power of 4, so you need at least 4 dimensions for a visual proof. Cannot be done!

Kojak