Recent content by ceptimus

The problem with that approach is that one brother has to wait at the eight mile mark for the motorcycle to arrive: Brother one: Walks four miles (60 minutes), then rides the motorcycle for four miles (16 minutes), takes car for final four miles (4 minutes) = 80 minutes total. Brother two...

Three brothers decide to exhibit their two vehicles at a vintage car and motorcycle show twelve miles from their house. They jointly own a single-seat car and a very early single-seat motorcycle. They are discussing how to get themselves and their vehicles to the show. "Our car goes at 60mph...

What is the point of storing Avagadro's number as an integer? We only know the first 8 digits accurately, so you will have fifteen zeros trailing after those digits. Languages like java, php, C# have a biginteger class that supports such large numbers, but I don't know about Fortran. You...

If you want accurate values, and you know how many decimal places you are working to, then you are better to store the numbers as integers. Say you want to work to three decimal places, then multiply all the numbers by 1000 and store them as integers. That way you will get exact results.

It's not so simple. It depends on the friction of the toboggan on the snow - which depends on the design of the toboggan, and the quality and temperature of the snow. And then it also depends on the air resistance of the toboggan and its rider(s). So there isn't a simple formula that...

The tyre won't put an even pressure on the ground over the whole contact area. Near to the edges of the contact area the pressure will be much less. You can prove this for yourself using a car tyre. Get a thin piece of plastic, such as an old credit card - you'll find that it's easy to slide...

I got it by a bit of algebra. I don't claim it helps in proving the statement, but (if it's right, as I think it is) then it allows anyone to guess any two values for b and c, and find the corresponding value of a that satisfies the first equation. It at least allows you to test the second...

I get: a = (1 - bc) / (2bc + b + c)

Yes. I was looking for the time when, if you call the angles between the three hands a, b, c, then the formula below has a minimum value: abs(120 - a) + abs(120 - b) + abs(120 - c) I think this occurs at roughly the time 02:54:34.576 perhaps a few milliseconds before or after. I...

Not quite. The second hand gets closer to the 120 degree position a couple of seconds after this time (and as the second hand goes round sixty times faster than the minute hand, the overall accuracy is better even though the minute hand is then a little off). That was the basis of my post, but...

It gets close enough for practical purposes at 02:54:34.576

You could use the other one to make 3^\infty

Concentrate on the left or right side of the ladder and ignore the other side. The vertical reaction from the floor has to support the weight of that half of the ladder. The weight of the ladder half acts vertically down, and as the ladder is uniform, the weight can be treated as a single...

ABCDEFGHIJKLMNOPQRSTUVWXYZ K..N.IYRCPC.SHUFDVGMA.OTL.

I can only do it with the forbidden square root. 93 = 4 \times 4! - \sqrt{\frac{4}{.\bar{4}}}