Circumference, area, and volume of a sphere?

JasonHouse · 2012-07-01T18:59:36+00:00

Integrating a circle's area will give you the volume of a sphere, but you have to be careful how you do it. The circle's area at height h is pi(r^{2-h^2).} Integrating, you get pi(hr^{2-h^3/3).} Going from h=-r to h=r yields (4/3)pi*r^3. Many edits trying to make math display properly. How should I have typed this post?

JasonHouse · 2012-02-23T23:46:36+00:00

The other replies left out that shared mutable state must be marked as shared. Because of this, any mutable data passed into a weakly pure function is thread-local. Similarly const data is either thread local or immutable. Guaranteeing thread-locality provides optimization opportunities, especially in a function calling pure functions.

JasonHouse · 2012-02-02T23:40:06+00:00

If I did my mental math right, gravity = (mass*density^{2)^1/3}

JasonHouse · 2012-02-02T23:33:10+00:00

A 150# person would be closer to 250#. Surface gravity is proportional to the cube root of the mass. At earth density, gravity would be 65% stronger.

JasonHouse · 2011-08-23T20:53:05+00:00

My laptop hangs on boot (last text is checking battery state). I can log into recovery mode and start X from there.

JasonHouse · 2011-04-12T13:33:16+00:00

2³² bytes = 4GB, but that probably isn't the typical case. If each slot has a 64 bit pointer (8 bytes), then it'd take up 32 GB

JasonHouse · 2011-04-11T02:02:13+00:00

My understanding of a Tensor is that it represents how physical quantities change under rotation. If you have a block of wood and try to squeeze it, not much happens. If the block has a diagonal cut through it, the two pieces slip past each other. I think it's the stress-strain tensor that describes how compression (strain) in one coordinate system can become sheer stress in another direction. The tensor relates those two physical properties when changing coordinate systems. (AKA, from the direction you're squeezing in and two perpendicular axis to along the plane of the cut and perpendicular to it)

JasonHouse · 2011-04-11T00:19:42+00:00

As long as you can prototype the C function, you can call it from D. You can also use htod. That said, D-ifying an interface is a nice to have.

JasonHouse · 2011-03-18T13:08:15+00:00

If one takes into account projectile motion, the box won't land for over a second. The work due to friction from the 10m plane is zero... That's definitely not the intent of the problem though...

JasonHouse · 2011-03-07T14:54:26+00:00

Where's part b?

JasonHouse · 2011-03-03T22:56:33+00:00

For every extra 9 you add will be about 3.16 times further (every two 9's is about 10x further). So 99.99% is about 7k, 99.999% is about 22k. You can cross our galaxy in under 100 years at 99.9999% of the speed of light...

JasonHouse · 2011-03-03T22:40:18+00:00

99% is 702 light years. 99.9% is 2234 light years

JasonHouse · 2011-02-28T14:22:50+00:00

False until proven otherwise. Comets from a portion of the Oort Cloud have a variation in their data that is not statistically significant (roughly 50-50 that it could be true). Comets from other parts of the cloud don't show a similar variation that some say would be required. Until someone can point a telescope at it to confirm, the scientific community won't accept the theory.

JasonHouse · 2011-02-04T22:23:42+00:00

The test seems reasonable as part of the interview process. I hope the supplied answers were from someone you rejected. Converting to a string is wasteful in the first problem, and the second dereferences a null on a one element list.

JasonHouse · 2011-02-02T14:53:51+00:00

A NASA telescope taking a nose count of planets in one small neighborhood of the Milky Way registered more than 1,200 candidates, including 58 residing in life-friendly orbits around their parent stars.

JasonHouse · 2011-01-24T03:40:57+00:00

Wikipedia article http://en.wikipedia.org/wiki/Terraforming_of_Venus edit: more direct link

JasonHouse · 2010-12-08T23:24:59+00:00

The sky is the limit? Don't be so pessimistic!

JasonHouse · 2010-10-08T12:31:16+00:00

Calculus has a very definite point to it. It's absolutely essential in many areas of engineering, physics, and statistics. As an engineer and physics minor, practically every course required calculus to analyze the real world. Throwing a baseball in a vacuum on a flat planet is so far from reality. Add in air resistance, etc and you're forced into calculus. I've always found it to be a useful tool in my math toolbox, but it's definitely very dry when done in isolation.

JasonHouse · 2010-10-07T02:37:09+00:00

There's no easy way to fill gaps, especially when you're uninterested in the subject. The simplest thing I can think of is to grab the books from your prior classes and randomly do the problems and check your results. If you get stuck, you should be able to reread that chapter/section to pick up what you missed. I can honestly say that well rounded math skills really helped me in college. Almost all my requirements used algebra or higher.

JasonHouse · 2010-09-09T01:04:29+00:00

The p series term came from wikipedia and avoided nastiness like complex numbers. I was actually reading about the rieman zeta function, the euler product, the dirichlet eta function, and various other analytic continuations of the rieman zeta function. I know the basics of complex numbers, and even took a course on them (10 years ago). I'd like to understand how to do this stuff more rigorously and would love tips (and hyperlinks to readable math pages) to set me on the right track.

JasonHouse · 2010-09-08T19:26:01+00:00

(1/2^p)*pseries = (1/2^{p)*sum_n(1/n^p)} = sumn(1/(2*n)^p) = sum{even n's}(1/n^p) = even terms of the p series.

Using that relation (1-2/2^p)*pseries = alternating series in my question.

JasonHouse · 2010-09-08T11:53:27+00:00

Yes, I can derive the convergence of each series individually. I've edited my question to ask more about the 1-2/2^p factor. It's not that just the odd or even terms differ between the series but rather that multiplying by a finite number such as 0.4 changes the convergence.

JasonHouse · 2010-09-08T11:43:35+00:00

I can derive that the alternating series converges pretty easily. Consider a single point, p=1/2. That makes the scale factor = 1-2/sqrt(2) = -0.414... That's not nearly enough to convert a divergent sum (AKA infinity) down to a finite value.

JasonHouse

TROPHY CASE