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Thank you ganesh,
I think I understand what it says on that ‘Maths Is Fun’ page. At least, I understand the logic of it. But I still don’t find it satisfactory. Have you or has anyone else got any philosophical comments about this phenomenon? It implies that 0.000…0001 is equal to zero, which doesn’t feel correct.
My wife and I had words yesterday. Though to be more precise, I had words and she had paragraphs.
I’m not saying my wife is bad at doing the housework but these days I have to wipe my feet on the front doormat every time I go out of the house.
My wife asked me for some peace and quiet while she cooked dinner, so I took the batteries out of the smoke detectors.
Hello,
I would be grateful if someone could explain to me the following please.
Since 1/9 = 0.11111….., does 9/9 = 0.99999….. or 1 exactly?
What is the difference between 0.9 recurring and 1.0 recurring?
I can’t get my head round this. At first glance it seems like a loophole in strict Aristotelian logic.
Thanks.
Isaac Newton must have been very surprised when that apple fell on his head. Especially since he was sitting under a pear tree at the time.
Dr and Mrs Pavlov decided they would have to get rid of their pet poodle because it kept dribbling on the new carpet in their lounge whenever the telephone would ring.
In 1878 when Joseph Swann came up with the idea of the electric light bulb, did a candle appear above his head?
Thanks very much, zetafunc. Your explanation is helpful. I watched your introductory video about continued fractions on your YouTube channel and that has stimulated my interest in that topic. I plan to watch more of your videos. Thank you for spreading your expertise and enthusiasm.
Jeremy
Well said, sajjadahmad!
I resonate with what you wrote. There is a coherence and elegance in math that points to something spiritual behind it and beyond it, something relevant to the foundation and structure of life, the universe, and everything. Mathematical patterns and equations are not inventions of men’s minds but discoveries of reality. We need a heart as well as a brain to fully appreciate math.
Thank you Ganesh for that extra interesting information about pi. But you still haven’t explained how we know pi has an infinite number of decimal places containing non-repeating digits. You stated that computers have calculated pi correct to 1.33 x 10^13 decimal places but how do we know the end is not just round the corner? Is it possible that one day a computer will calculate the exact value of pi to a finite number of decimal places?
Why did the chicken cross the Möbius strip?
To get to the same side.
So how do we know that pi has an infinite number of decimal places that never repeat? I mean, if the fastest modern computers have not yet calculated the last decimal digit of pi, how do we know that the end is not just one or two decimal places further on?
Sorry if that’s a silly question!
Hi Phro and Bob,
Very interesting to read your two approaches. And that is impressive software!
I have given up trying to solve this myself. It is far above my ability. I had thought that because it was included in the Maths Is Fun puzzle pages, it would be fairly easy to solve with a bit of basic knowledge and effort. But googling the problem has revealed to me that it has taxed some very advanced mathematicians over the centuries. There seem to be numerous ways of solving it and I don’t understand any of the detailed explanations of the solutions! Guillaume François Antoine de l'Hôpital himself solved it using calculus but other methods exist.
Before I started this thread I searched past posts on this forum to see if this problem had been discussed before. I did not find anything but this morning I came across this thread in the course of my google search: previous discussion.
By the way, I confirm your answer to the problem. Relying on trigonometry I used my calculator to work out the various altitudes of the weight depending on different angles of BAC, and I repeated the laborious calculation to gradually home in on the maximum result. I got the answer to be 51.90438 to 5 decimal places. This method gives the right answer but in the most boring and prosaic manner possible. It misses out on the beauty and elegance inherent in math.
If you have any more insights on this problem I will be interested to hear your thoughts.
Jeremy
Thank you, Bob, for your welcome and for the hints about the puzzle. I will follow your guidance and see if I can make any progress.
The Marquis de L’Hopital was a brilliant French mathematician of the 17th century. I find the lives and work of ancient mathematicians fascinating. This puzzle was published in his famous textbook on calculus.
Thanks again for your help.
I’m not saying my wife is overweight but whereas some people call their wife ‘My other half’, I call mine ‘My other 9/10ths’.
My wife got a mud pack. She looked great for two days. Then the mud fell off.
My wife kept complaining that my snoring kept her awake at night. But I’ve managed to solve the problem. I bought a pair of ear plugs and so now I can’t hear her complaining.
Hello,
I have been studying some of the Maths Is Fun tutorial pages to brush up on my math knowledge and skills. (I studied math at university 40 years ago but haven’t looked at it since. Now that I am retired from work I want to delve back in to the world of math.)
I came across an interesting puzzle here: Maths Is Fun puzzles and I have been wrestling with it but getting nowhere. I would be very grateful for a hint of how to begin to solve it please. But I don’t want to be spoon-fed the answer.
Thanks very much in advance.
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