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What is a trapezoidal shaped section of a sphere or ellipsoid's surface called? I think it is something like "quadratic angle" or "quadrilateral section"—?
~Kaimbridge~
01:04, 13 December 2006 (UTC)
No, that's not the term (I came across the term and an image of it a while back, while looking something else up——I think either here in Wikipedia or MathWorld).
The closest description would be "spherical isosceles trapezoid" (but, like segments in the above image, not necessarily "upright").
~Kaimbridge~
20:11, 13 December 2006 (UTC)
It doesn't have to be: See image——any of those grid sectors qualify.
No, like I said, I came across the term/diagram in some math source. Oh well, I'll likely see it again (when I least expect it! P=) ~Kaimbridge~ 17:29, 18 December 2006 (UTC)
Hi all! I think this is a simple question, but I cannot think a clever algorithm for this problem: We will work in standard x-y-z space. We have an objective (strictly positive and bounded) function f(x,y) in domain, says, [0,10]x[0,10], and we want to write a computer program to find the set of all points {(x,y) } in the domain which locally maximizes f(x,y). However, suppose f(x,y) contains many many local maximum points, says, more than hundred mountains in the domain. To simplify the problem now, I suppose there is no ridge in any mountains.
Let us suppose that we can calculate the gradient (and hessian) of f(x,y), my basic scheme is to try using standard gradient ascent (or conjugate gradient, etc.) many times with different random starting points to discover all mountains. However, suppose my 2 answers (x1,y1) and (x2,y2) are very closed, and also f(x1,y1) and f(x2,y2) are also very closed. How can we check that they come from the same mountain (but with small numerical errors), or they really come from two different mountains?? -- 131.111.164.218 12:55, 13 December 2006 (UTC)
I need assistance determining the the TRUE ROI for a serious of investments with differing profit/loss and differing capital injections.
For example:
Jan 06: Purchase $10000 in shares in X Jan 06: Sell all shares in X and make profit of $1000 & spend this $1000 Feb 06: Take $10000 & purchase share in Y Feb 06: Stock drops and purchase $5000 more share sin Y Mar 06: Sell all shares in Y & make profit of $1500.
Individually, the SIMPLE ROI for each investment is 10%
However, the total profit is $2500, with a maximum invesment of $15000 = 16.7% return. I think this is wrong.. I need validation
OR
Do i just weight each investment accordingly to better understand the correct SIMPLE ROI.
OR
Is there some other method to best figure out ROI?
Thanks Trevor Gartner trevor.gartner@telus.com
I'd say the ROI is actually closer to 18%, because you only actually invest 14k (the 1k you gain after the first "session" can be deducted from the 5k extra you put in). yandman 20:50, 13 December 2006 (UTC)
The five postulates of classical Euclidian geometry are
By changing the fifth postulate, you get the hyperbolic and elliptical geometries. But what sort of geometry do you get if you change the fourth postulate? -- Carnildo 23:49, 13 December 2006 (UTC)
As a bit of a cheat - how about if the three orthogonal vectors ie i,j,k are replaced by sheared versions eg i'=i,j'=0.9j+0.1i,k'=0.9k+0.1i+0.1j ? (needs normalising) so then the new 'right angles' would be angle between vectors i'j', i'k', and j'k' - so the new angle bewteen two vectors would be calculated from the 'new right angle' would vary depending on the orientation of the two vectors - not really what you are looking for I suspect..(Though it does make the new 'right angles' non congruent in euclidean geom) 83.100.174.70 19:53, 14 December 2006 (UTC)
Mathematics desk | ||
---|---|---|
< December 12 | << Nov | December | Jan >> | December 14 > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
What is a trapezoidal shaped section of a sphere or ellipsoid's surface called? I think it is something like "quadratic angle" or "quadrilateral section"—?
~Kaimbridge~
01:04, 13 December 2006 (UTC)
No, that's not the term (I came across the term and an image of it a while back, while looking something else up——I think either here in Wikipedia or MathWorld).
The closest description would be "spherical isosceles trapezoid" (but, like segments in the above image, not necessarily "upright").
~Kaimbridge~
20:11, 13 December 2006 (UTC)
It doesn't have to be: See image——any of those grid sectors qualify.
No, like I said, I came across the term/diagram in some math source. Oh well, I'll likely see it again (when I least expect it! P=) ~Kaimbridge~ 17:29, 18 December 2006 (UTC)
Hi all! I think this is a simple question, but I cannot think a clever algorithm for this problem: We will work in standard x-y-z space. We have an objective (strictly positive and bounded) function f(x,y) in domain, says, [0,10]x[0,10], and we want to write a computer program to find the set of all points {(x,y) } in the domain which locally maximizes f(x,y). However, suppose f(x,y) contains many many local maximum points, says, more than hundred mountains in the domain. To simplify the problem now, I suppose there is no ridge in any mountains.
Let us suppose that we can calculate the gradient (and hessian) of f(x,y), my basic scheme is to try using standard gradient ascent (or conjugate gradient, etc.) many times with different random starting points to discover all mountains. However, suppose my 2 answers (x1,y1) and (x2,y2) are very closed, and also f(x1,y1) and f(x2,y2) are also very closed. How can we check that they come from the same mountain (but with small numerical errors), or they really come from two different mountains?? -- 131.111.164.218 12:55, 13 December 2006 (UTC)
I need assistance determining the the TRUE ROI for a serious of investments with differing profit/loss and differing capital injections.
For example:
Jan 06: Purchase $10000 in shares in X Jan 06: Sell all shares in X and make profit of $1000 & spend this $1000 Feb 06: Take $10000 & purchase share in Y Feb 06: Stock drops and purchase $5000 more share sin Y Mar 06: Sell all shares in Y & make profit of $1500.
Individually, the SIMPLE ROI for each investment is 10%
However, the total profit is $2500, with a maximum invesment of $15000 = 16.7% return. I think this is wrong.. I need validation
OR
Do i just weight each investment accordingly to better understand the correct SIMPLE ROI.
OR
Is there some other method to best figure out ROI?
Thanks Trevor Gartner trevor.gartner@telus.com
I'd say the ROI is actually closer to 18%, because you only actually invest 14k (the 1k you gain after the first "session" can be deducted from the 5k extra you put in). yandman 20:50, 13 December 2006 (UTC)
The five postulates of classical Euclidian geometry are
By changing the fifth postulate, you get the hyperbolic and elliptical geometries. But what sort of geometry do you get if you change the fourth postulate? -- Carnildo 23:49, 13 December 2006 (UTC)
As a bit of a cheat - how about if the three orthogonal vectors ie i,j,k are replaced by sheared versions eg i'=i,j'=0.9j+0.1i,k'=0.9k+0.1i+0.1j ? (needs normalising) so then the new 'right angles' would be angle between vectors i'j', i'k', and j'k' - so the new angle bewteen two vectors would be calculated from the 'new right angle' would vary depending on the orientation of the two vectors - not really what you are looking for I suspect..(Though it does make the new 'right angles' non congruent in euclidean geom) 83.100.174.70 19:53, 14 December 2006 (UTC)