dalgoma

It has to be Meccano!

Assuming that the air in tyres is at 2 bars, you would be releasing twice the volume into the atmosphere and replacing it with CO2 would isolate quite a lot of CO2!

If all the tyres of all the vehicles in the world was replaced with CO2, what would it do for global warming?

A falling weight. And the power available need not necessarily cease when the weight reaches the end of its travel ... http://monologues.co.uk/004/Bricklayers_Story.htm

Regarding the disc viewed edge on:- Although the line has no width, it does have length - and that is information, not nothing. Viewed from the disc edge, the line is a tangent of infinite length. Unless viewed from infinity its length is always greater than the diameter of the disc. When viewed from infinity it is nothing.

Joining the 8 vertices of one cube on top of another has got a certain logic :- View a square to a corner you see 2 lines View a cube to an edge you see 2 squares View a 4D cube from a chosen location you see 2 cubes. By choosing the viewpoint we seem to be able to obscure a dimension.

4 D CUBES<BR style="mso-special-character: line-break"><BR style="mso-special-character: line-break"> To construct a cube, we join 2 squares together with 4 lines each the same length as the side of the square to each of the vertices. If we put one cube on top of another, we can join the 8 vertices with lines of the same length as the side of the cube. Is this a 4D cube? If not why not!

Wow, I like the link. But I don't think it is much to do with the focal length of the lens. Can we agree that, apart from the obvious grain, a photo taken with a long focus lens is indistinguishable from the centre of one taken with a wide angle lens at the same location. The only way to change the perspective is to move.

The following was written by Peter Hilton, Mathematician at Bletchley Park in 1943, one of the Emigma codebreakers. "Doc note, I dissent. A fast never prevents a fatness. I diet on cod" A coincidence- I have just noticed that Peter Hilton died on Dec. 2. http://www.guardian.co.uk/science/2010/dec/02/peter-hilton-obituary

Yes. And if you drilled a 1 metre long hole through the middle of a earth sized sphere, the volume left would be equal to that of a 1 metre diameter sphere without a hole.

I put the picture plane at the centre of the circle to make the maths easier when evolving the formula. This figure shows another circle as well as their surrounding squares - and yes indeed, the centres are at the intersection of the diagonals of the squares.

For Tony. Absolutely right! For Michel- The construction is my own and seems to me simple, have a certain mathematical elegance and satisfies observatioin. However, I cannot at the moment relate it to the projection of a particular circle at a particular location. What it does do is predict the tilt angle of an elliptical image whose centre P is in that position in relation to O whatever its size. Also I cannot establish major an minor axes. For instance, if we plot the image of concentric circles, They would not share the same common centre. Hence, they would have their own tilt angles if the were not on CoV. Can I suggest that you view CiP 2. This produces circular images! and they are generated by projection from plan and section in the traditional way. I would be interested in your comments.

Yes, I should have said "without so much loss of definition" Like the old days you chose a slow speed film for a fine grain if you wanted to enlarge. Ah, there is the rub! In all my constructions I have assumed a flat picture plane normal to the line of sight in both planes. Just like a camera that does not move.

Michel, Thank you very much for your input, I very much appreciate it. Is that what we call anamorphism? - Like the skull in Holbein's "The Ambassadors". If magnification does occur why does a raptor not use it? Merely focusing does not make things bigger, having more rods or whatever in its retina dosen't either - it just makes magnificatiion possible without loss of definition. As you know log. spirals are closely allied to the fibronacci series used so much in nature from the breeding cycle of rabbits to the arrangments of tree branches and dare I say, architecture, apporoaching the proportion 1:1.6180933... I posted to a falconry forum a received this reply - Great post ! I do not believe they see things at a distance as larger due to the fact of calibrating the distance to acquire the quarry. I have to agree that maybe in fact the eye Zooms in and out like the Lens theory. This has often fascinated myself. But also as I have hawked over many years and I have often wondered when you kick up a Rabbit and it does a wing over and crashes the brush after a snake ? I have certainly have seen some odd things while hunting with a BOP. Surley, the bird would not have seen the snake if it was solely focused on the rabbit. We may have exhusted this subject. I only raised it when looking at the views of Circles in Perspective. It is fun though! .

no we don't! see for example http://www.math.utah.edu/~treiberg/Perspect/Perspect.htm#circle