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Cylindrical Cuts (Posted on 2009-01-22) Difficulty: 4 of 5
An object resembling that in the graphic, is carved from a cube of soft material such that its elevations, as seen from the top, front and side, are all that of the drawing at the top.

Note that each curve is a segment of a quadrant circle centred on the opposite corner and having the radius of the side of the square.

While the object may look like a stellated octahedron, each curved stellated extension is actually formed by six surfaces being parts of cylindrical forms (thus there are 48 actual surfaces which form the object).

What percentage of the cube is wasted to create this object?

"Impossible" Solid's Volume was a somewhat related problem.

See The Solution Submitted by brianjn    
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re: numerical integration -- note on programming language | Comment 2 of 5 |
(In reply to numerical integration by Charlie)

Explaining why the QuickBasic integration came out different from the VB integration with step size .0001:

Even though DEFDBL A-Z was coded into the QB version, so that variable stp was double precision, the line

stp = .0001

placed a single precision constant into it.

Recoding as

stp = .0001#

corrected that, and the results are the same as the VB version. The # makes the .0001 accurate to double precision accuracy.

 

 


  Posted by Charlie on 2009-01-22 16:44:36
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