alan2here

I recently descovered a materal apparently called clinker. It's a deep purple color, a little reflective and has the apperance of ceramic, stone\brick and metal. It is irregular yet smooth and reminds me of expensive underused materals such as marble. It is however apparently free and considered always to be just a waste product.

A conventional house, made of bricks, wood, metal pipes etc... takes many professionals a long time to construct and so is expensive for labour costs and relies on there being people with these skills available. If the process was simplified but kept to resemble a conventional house, for example: Bricks shaped like jigsaw pieces at either end requiring no cement. Those bendy pipes made of many small segments like the sort you get for showers that screw on either end. etc... such that the house could be built by anyone from simple instructions then do you think the extra cost of production would outweigh the labour cost saving?

I thought everything was like a float not an integer by default as it is algebra.

In this link. What do the #'s in the solution mean? Also there could be 0 to 4 solutions for given values of x, q, w, r, t and u. How do the equations provided return those up to 4 values?

Imagine standing on the equator (I forgot to mention that part) and you go east or west, your angle relative to the north pole is pi/2 and the same at all times. Now imagine standing anwhere and going north, again your angle to the north pole always stays at 0 untill you cross the north pole. This time you are standing 10 meters from the north pole, you travel at an angle of pi/2 10 meters. You are now further away from the north pole but not as much further as if you have traveled directly away from it (angle of pi). Your angle relative to the north pole is different from when you started, it is your final_angle. To be the same as the angle variable in this case the man would have had to move in a curve, but he didn't he moved in a straight line.

Only on a map, not on a sphere or the "faulty_latitude_move" code would work. Continuing with the globe analogy he starts in England, turns to the north and moves some distance getting him close to the north pole, in this case his angle relative to the north pole would not change. If he were to move east or west putting him in the ocean or the direction of Russia the result would be the same. However if he turns to face north east then moves you would not expect his angle relative to the north pole to stay the same. It's going to start at 1/8th of a turn clockwise and end up at 1/4 of a turn when he is north of Russia, imagine this happening on a globe. Very visually. It's going to be easy to see if it has worked.

inputs: sphere in space: x, y, z, radius man on sphere: latitude, longitude man's intention: angle, distance faulty_latitude_move = sin(angle) * distance faulty_longitude_move = cos(angle) * distance latitude_move = arcsin(sin(angle) * sin(distance\radius)) longitude_move = arcsin(sin(angle) * sin(distance\radius)) final_latitude = latitude + latitude_move final_longitude = longitude + longitude_move final_z = z + (radius * sin(final_latitude)) final_x = x + (radius * cos(final_latitude) * cos(final_longitude)) final_y = y + (radius * cos(final_latitude) * sin(final_longitude)) final_angle = angle outputs: man on sphere: final_latitude, final_longitude, final_angle man in space: final_z, final_x, final_y Horray, see the old version labled faulty and the new version at the top. Now only one more part to do: final_angle = angle

Do 'a' and 'b' help the rest of the function at all? btw the function should work for moving east around the sphere and north, it's only when moving diagonally that there may be a problem, which is that the man will curve towards the poles. The other problem is that final_angle will produce the wrong answer.

Corrected below. inputs: sphere in space: x, y, z, radius man on sphere: latitude, longitude man's intention: angle, distance a = arcsin(sin(angle) * sin(distance\radius)) b = arcsin(sin(angle) * sin(distance\radius)) final_latitude = latitude + (sin(angle) * distance) final_longitude = longitude + (cos(angle) * distance) final_z = z + (radius * sin(final_latitude)) final_x = x + (radius * cos(final_latitude) * cos(final_longitude)) final_y = y + (radius * cos(final_latitude) * sin(final_longitude)) final_angle = angle outputs: man on sphere: final_latitude, final_longitude, final_angle man in space: final_z, final_x, final_y angle is the angle the man is facing in radians relative to the north pole final_angle is angle the man is facing in radians relative to the north pole after he has moved distance in angle direction etc...

90 degrees is 1.57 radians, sin(1.57) = 1 Thanks, looks like I miscalculated that first time somehow. I simplfied out the devide by 1. How do I interface the parts together? Green represents placeholder code that's not entirely accurate. Blue represents code that's not part of the forumuli yet. sin_a = sin(angle) * sin(distance) sin_b = sin(angle) * sin(distance) a = 2 * pi * sin_a + arcsin(sin_a) b = 2 * pi * sin_b + arcsin(sin_b) o1 = a/2 o2 = b/2 final_latitude = latitude + (sin(angle) * distance) final_longitude = longitude + (cos(angle) * distance) final_z = radius * sin(final_latitude) final_x = radius * cos(final_latitude) * cos(final_longitude) final_y = radius * cos(final_latitude) * sin(final_longitude) final_angle = angle

Cool, trigonometry is not that hard, the solution I preposed in my last post uses it. Ok, lets try that. radius = 2 latitude = equator = 0.5 longitude = 0 angle = 0.3 distance = 1 I'm working in radians [math]sin a = sin 0.3 * sin 1 = 0.25[/math] [math]sin b = sin 1.27 * sin 1 = 0.8[/math] Wolfram Alpha told me that "a = 2 * pi * n + sin^-1(n)". sin^-1(n) = arcsin(n)? a = 1.82 b = 5.95 o1 = 1.82/2 = 0.91 o2 = 5.95/2 = 2.98 I'm not sure how to do this bit. Also nothing functions in degrees. which values corispond to the required outputs?

Thanks. I may try Buttacups solution, it could take a long time to implement. Buttacup, does your latest post add onto the post before or is it a solution in itself? Whats the Euler rotational matrix, a component of Buttacups solution or a whole solution? Will the following work instead? final_latitude = latitude + (sin(angle) * distance) final_longitude = longitude + (cos(angle) * distance) final_z = radius * sin(final_latitude) final_x = radius * cos(final_latitude) * cos(final_longitude) final_y = radius * cos(final_latitude) * sin(final_longitude) final_angle = angle This should be unfortunatly distorted as it presumes the N, S, E & W you would get on a map not a sphere. But it seems braudly correct, provided the equation from here that it is based on is correct.

For this: z (up & down) = r sin(lat) x = r cos(lat) cos(long) y = r cos(lat) sin(long) (0, 0, 0) is not in the center of the sphere, it's on an edge? and the sphere moves left and right depending on the latitude chosen? Might not be a particularly hard problem but seems odd. Merged post follows: Consecutive posts mergedSo the matrix way does get me all the angles and things specified in the first post as outputs when given the input parameters specified?

C++ std library. I have coded matrix multiplications before, but this is on just one point, in quite a simple way, where the point starts in a place defined by a simple equation before it is moved. I'm sure it doesn't need all the little things that could go wrong, take a long time to do, may require dependency on other libraries and are hard to test with matrix transformations. Especially as I don't have much of a maths background and this is the only part of the whole program that needs any part of the calculation.

If I must code up complicated matrix stuff is there one transformation matrix that I can use instead of 3 in a row?

Thanks, looks like it would make a good question for one studying maths, hard with various possible methods of doing it covering all sorts of stuff. I can use this equation from the article to create a simple verstion of the problem. x = r Cos[lat] Cos[long] y = r Cos[lat] Sin[long] z = r Sin[lat] This will be ok as a placeholder for now. I tried to create a similar equation but it was not as good as my sphere was lemon shaped. Merged post follows: Consecutive posts mergedSo I know I'm correctly oriented, for using this equation, with trigonometric functions that use radians. z = up\down latitude of -pi*0.5 = north pole latitude of pi*0.5 = south pole longitude of 0 is the same place as a longitude of pi.

This is for a coding project I'm working on. It's not to do with men walking on spheres but it's a good way of describing the problem. Can anyone produce equations, code or similar to calculate outputs for given inputs. Inputs are: x, y & z coordinates of the spheres center radius of the sphere start latitude coordinate of the man start longitude coordinate of the man start angle of the man distance for the man to travel For the following scenario: Imagine the sphere centered at given coordinates where the north pole is at the topmost point. A man stands on the sphere at the latitude and longitude specified where 0 latitude is the north pole, 1 latitude is the south pole and ±1 longitude rotates east\west once around the sphere. He is facing a specified angle where 0 and 1 are facing the north pole, 0.5, 0.25 to the east, 0.75 to the west etc... he walks the specified distance around the sphere from his point of view in a straight line in the direction he is facing where 1 represents once round the largest part of the sphere such as the equator. I then need to be able to get the following outputs: final x, y & z coordinates of the man final latitude coordinate of the man final longitude coordinate of the man final angle of the man The mans start angle will definitely be equal to his final angle if the distance traveled is a multiple of 1 or he starts with a latitude of 0.5 and an angle of 0.25 or 0.75 representing him going either way round the equator. Similarly going away from or towards the poles without passing them would show no change in angle.

Thanks. It's a differnt way to describe binary numbers. Merged post follows: Consecutive posts merged Thats a verry confusing looking equation. Yes, this makes sence. Thanks. I see now how the equation works now (b = base) A = 542 = A2*b2 + A1*b1 + A0*b0. 542 = [math]\sum[/math]Anbn So an equation calculates how many differnt K of N combinations exist is. [imath]\frac{n!}{k!\,(n-k)!}[/imath] edit: seems to work.

That can already be done. With functions smaller than genes, short sequences of base pairs put together to create a DNA strand that describes a functioning lifeform and implanted into a cell that is designed to loose it's identity and become as described by any DNA that it encounters.

I see, binomial coefficients? I've never come across this before. How would the number 4 be represented in this notation? Merged post follows: Consecutive posts merged Thanks. This means that the central row of each one shows digitally balanced numbers, with varying degrees of imbalance towards the top and bottom. I think the [imath]\cdot[/imath] operator means multiply? It's every other one instead. Seems I was wrong, it does appear as if there is some pattern of prime distributions though. Seems to much of a coincidence. Wolfram alpha shows that several rows including the middle one (digitally balanced numbers) produce a fractal like graph.

I'm confused by this. Various TED talks, the video "DNA Hacking" as well as at least one "Futures in Biotech" episode all sugest that the following things have been possible for some time. Reading DNA into a computer file. Creating DNA from a computer file. Implanting DNA into a cell that has been designed to morph to match the DNA. The sending of samples to be read, DNA or a cell made from DNA of your choosing being sent by mail order. Storing sequences as a "component" and combining them to abstract other components and more ambitious functionality. The abbilty to look up any of these components online and get there base pair sequences. Performing more complicated queries on archives of base pair series from animals including humans. Projects to refactor functions found in DNA so that for example two functions don't overlap and to document them. etc... Which leaves me wondering is this somewhat old news that journalists have only just noticed? Or there is something new that was just to technical to elaborate on much. Despite the talk of human error and terror etc... that the BBC seems to have made up it seems positive to inform the public of progress.

I should imagine that a building could be constructed like this to be extremely tall. Although given the angles of the cables they would have to be extremely long. Given that the diameter of the earth is 12756.2km and the angles and heights of the cables proportional to the height of the building, one could work out the tallest possible building of this design.

The 2nd row is an ordered set where [math]s_{n}[/math] = [math]2^{n}[/math]. How is it the sum of something times by [math]2^{n}[/math] where n is the sum counter? Isn't that going to return a number? Are you saying that for subsequent elements in the sequence this observation of primes wouldn't hold true?

Take the binary numbers of a cirtain length, for example. 00 01 10 11 Sort them into how many 1's they have. 00 01, 10 11 Write them in a more familiar form. 0 1, 2 3 And you have a pattern of numbers, which is more interesting with larger examples. 0 1 0 1, 2 3 0 1, 2, 4 3, 5, 6 7 0 1, 2, 4, 8 3, 5, 6, 9, 10, 12 7, 11, 13, 14 15 The first and last rows contain one element. The 2nd row shows powers of 2. More interestingly in all cases all but the last element of the 2nd to last row are prime.

Something reminded me of this remarkable building recently. http://farm2.static.flickr.com/1053/1488454529_cc202cbd73.jpg It must have an aspect ratio of a million to 1, with weight reasonably distributed along it, including at the top, and yet it stands.