Garderners question time :)

I am just about to lay a new lawn, it is 15 sq metres and i need to  level the ground by 8cm all the way round. I have ordered 1.2 cube of compost will this be enough, how do i work out the volume required???

Dictionary.com says a billion is "a cardinal number represented in the U.S. by 1 followed by 9 zeros, and in Great Britain by 1 followed by 12 zeros." It also seems it indicate that British definition is no longer used, although it's unclear on that.

Does a billion still represent two different numbers among scientists? If not, when did this change? Wouldn't older papers still use the old definition? Has this discrepency caused any practical problems in scientific projects--particularly in relation to astronomy and physics?

Cheers,

John

How many lottery tickets would have to be bought for there to be a >=50% probablility that every single possible combination has been chosen?  Or for smaller numbers how many people would you need in a room for there to be a >=50% probability that every day of the year is one or more of these people's birthdays?  

If these numbers are too large then how many people/tickets would be needed that there is a >=50% probability that >=50% of the lottery tickets/birthdays have been chosen?

Assume that birthdays and lottery tickets are chosen at random and not bunched, and forget about leap years to keep things slightly simpler.

I have read a lot of articles on the use of parabolic mirrors to focus light to a central tower, such as the article in 11 Dec 2010 on Gemasolar; but how can these mirrors be parabolic?  A parabolic mirror will focus towards the center of the dish, which is why solar ovens put the food chamber in the center at the focal distance and towards the sun and  TV dishes have the collecting devices in front of them towards the incoming signal.  These dishes are all around the central tower, so some will have their front to the tower, some to the side, and some to the back (so to speak) of the incoming sun.  Even shifting the angles of the mirrors would not allow the focus to be towards the central tower, but towards the location of the sun.  Since the tower can not be in many places at once, how do all of these dishes focus to the central tower?

Mathematically, this is sum of zeros. All definitions of a line are that it has no “width” but should it also be true that it should ahs no “length”?

Is this true?

Does anyone have a sensibly worded explanation as to why the alternate numbers of a multiple of eleven have the same sum?

e.g 312741  =  11 x 28431

3+2+4=1+7+1=9

I have given this some thought and have not been able to word it to an understandable degree.

It's generally said that QWERTY keyboards were originally designed to be inefficient, to slow down some keystrokes to prevent jamming of typebars in mechanical typewriters. On the other hand, there are some free market think tanks that claim the QWERTY keyboard really is the most efficient, though their claims may be biased. 

Being old enough to have used an old "typebar" typewriter, the most common jams I seem to remember were associated with typing numbers such as "12" (which might be consistent with Benford's Law). If an empirical approach was used to prevent jams, one might have expected the numbers across the top of the keyboard (or separate calculator-like keypads, if such machines used similar mechanisms) to have been scrambled as well (though old typewriters did seem to use something like the letter "I" for the number one).

Since one commonly hears people bringing up QWERTY keyboards as an example of "entrenched inefficiencies," has newer technology (and the advent of "thumb typing" and the like) caused new keyboard formats to flourish?

I can verirify that every nunber in a list is prime, but how can I prove (without recourse to an existing list - which i would have to take on faith) that no prime has been omitted?

I decided to find out how many results Google returned when performing a search for numbers 0-10. All of them returned results between 7-17 billion, apart from 9, which returned less than 1 billion.  Can anyone think why?