Scythian1950

This is a shameless rip-off of Rita the dog's posted question:

http://answers.yahoo.com/question/index?qid=201401...

Now, for any real a, b, c, the following parametric equations:

http://i254.photobucket.com/albums/hh120/Scythian1...

...is that of a perfect circle as t = -∞ to ∞. Can you show that this is indeed a circle, and what's the best way to show that?

Check graphic of a 12" diameter pizza with 3 straight cuts, leaving a right triangle piece in the center.

http://i254.photobucket.com/albums/hh120/Scythian1...

The arcs in degrees are to be one of each {15, 30, 45, 60, 90, 120}, totaling 360, in some order, not necessarily progressive. The graphic shown doesn't show correct arcs, do not rely on the graphic to assign arc degrees. What's the exact maximum area, in square inches, can this right triangle piece in the center can have? Please express your answer in this form:

A + B√2 + C√3 + D√6

where A, B, C, D are rational numbers, positive or negative.

An arc in degrees is the angle subtended from the center of the circle, not angles formed by intersection of cuts.

Check out graphic of pieces:

http://i254.photobucket.com/albums/hh120/Scythian1...

On the left is a piece composed of 7 small cubes as shown, and on the right is 1 small cube. You have 3 of the pieces on the left, and 6 small cubes. Is it possible to assemble these 9 pieces together into a 3 x 3 x 3 cube? The 3 pieces that are composed of 7 small cubes are identical, no mirror copies are allowed. All small cubes are of the same size, so that:

3 pieces composed of 7 small cubes each = 21

21 + 6 small cubes = 27 = 3 x 3 x 3 cube.

Check out Rush Limbaugh's own website on his comments about the polar vortex, which he claims is a "made up new thing by liberals".

http://www.rushlimbaugh.com/daily/2014/01/06/left_...

Here's a 1985 meteorologist map of a polar vortex, per wiki:

http://en.wikipedia.org/wiki/File:Polarvortexjan21...

Is there anybody out there that agrees with Rush Limbaugh that this is simply a new hoax, to push a liberal agenda?

A great many clever proofs have been devised for the classic a² + b² = c² Pythagorean theorem. Given a tri-rectangular pyramid, composed of 3 right triangles A, B, C meeting at a common orthogonal vertex, with a triangular base D, it is also generally true that A² + B² + C² = D², where A, B, C, D are the areas of those triangles. Can you find a clever proof for this?

BA goes to best effort.

Check out graph of tri-rectangular pyramid, orthogonal vertex is on left bottom:

http://i254.photobucket.com/albums/hh120/Scythian1...

It has always been difficult to reply to Yahoo email whenever I get a message via my AOL email address. Now it seems impossible, I can't seem to send any reply at all. Is there a way to find out the direct email address of Yahoo users using Yahoo to send emails?

I get the impression that Yahoo is trying to force me to use ONLY Yahoo mail.

Find angle X, see graphic:

http://i254.photobucket.com/albums/hh120/Scythian1...

Let k = 4n, where n = positive integer.

Let a = x + √(x² - k²) and b = x - √(x² - k²). Prove that as positive integer n -> ∞,

(1/2) (1/k^k) (a^k + b^k) -> Cos(x)

Check out plot of both functions for n = 10, a small number:

http://i254.photobucket.com/albums/hh120/Scythian1...

See graph of 2 functions, √(1 - (x -1)² and x√(1 - (x -1)²

http://i254.photobucket.com/albums/hh120/Scythian1...

Prove that they have the same area. Maybe you can do this without calculus?

Most everybody thinks that winter solstice (usually Dec 21) is when both earliest sunset and latest sunrise occurs (in northern hemisphere), but that's not true. Earliest sunset occurs in early December, and latest sunrise occurs in early January. Why is that?

Winter solstice is when the day is shortest, i.e., time between sunrise and sunset.

Amplituhedrons are now probably the most exciting development in theoretical physics. It's said that with amplituhedrons, perhaps finally quantum gravity can be married with quantum field theory, through removal of the need for locality and unitarity as "fundamental properties".

Any opinions about amplituhedrons?

Find the integer lengths of squares a to n. See graphic:

http://i254.photobucket.com/albums/hh120/Scythian1...

I'd like to see how this can easily be determined.

Given a and b, prove that for maximum angle Φ, c = √(ab) without using calculus. See diagram:

http://i254.photobucket.com/albums/hh120/Scythian1...

Check out these photographs of churches:

http://www.slate.com/blogs/behold/2013/10/13/richa...

The photographer is effectively projecting the ceilings and walls of these churches onto a cylinder which axis is perpendicular to the main centerline of the churches. Given that these churches have the following geometrical elements:

1) Horizontal lines running parallel to the main centerline

2) Horizontal lines running perpendicular to the main centerline

3) Vertical lines running orthogonal to 1) and 2)

What families of curves are 1), 2), and 3) are making?

Note: Many of the "vertical columns" veer off on separate curves at the top, disregard those separate curves. Only consider the orthogonal straight line elements 1), 2), 3)

The integer edges of a non-cube box adds up to A. The areas of this box adds up to B. For the given A and B, this box has the minimum volume. What's the volume of this box?

To make this clearer, for example, for a box with dimensions 3, 4, 5, A = 48, and B = 94. But the volume, 60, isn't necessarily the minimum for given A and B, if the sides are different from 3, 4, 5.

An elastic track on the ground is of length 1, fixed at the start position, the other end pulled by a tractor so that the track stretches uniformly. At time = 0, a runner is at the start position, and begins running at constant speed v on the track. The tractor also begins pulling at constant speed v. Prove that when the runner reaches the tractor, the track is of length e, or Euler's number.

Seven men go to a bar to have a party. The first guy says he'll pay for 1/2 of all the drinks. The second guy says he'll pay for 1/3 of all the drinks. The third says he'll just pay for his own share, or 1/7 of all the drinks. Everybody drinks the same amount, except the one guy that is the designated driver, who doesn't have any drinks at all. Late into the night when the waiter gives them the final bill for $410, the men get into a drunken squabble over the bill because neither 3 or 7 divides into $410. Finally in exasperation the waiter says, "Look, I'm going to add an extra $10 to your bill so you guys can do your math!" This makes the drunken men happy because then the first guy pays $210, or 1/2 of the bill, the second guy pays $140, or 1/3 of the bill, and the 3rd guy pays $60, or 1/7 of the bill, as agreed. The total comes to $410, and so it turns out that the waiter was able to take off that extra $10 from the bill after all.

So, who got cheated?

What's going on? I'm finding it harder and harder to navigate Y!A, and certain problems like dropped "+" signs are still not fixed. We can't leave comments like we used to, there is no follow up. Is Y!A trying to drive away the math regulars?

See diagram:

http://i254.photobucket.com/albums/hh120/Scythian1...

A draftman has a circle of radius 2 drawn, centered on perpendicular axes as shown. One point is (0, 10/3), the other is (6,0). He wishes to find the point on the circle such that the line from one point is reflected from the circle at the unknown point towards the other point. Can he find this point by using a straightedge and compass?