Math Is Fun Forum

Thanks, bobbym - I've never heard of them being a class of "Latin Squares" before - but I see what you mean.  Thanks.

I recall looking cosh and sinh up in Wikipedia.  If I remember correctly, they describe the way a rope hangs between two points, called a catenary.  Worth a look for yourself?

Thanks for the answers - so it seems if one tried to define some "new maths" involving ln(-1) it would turn out that sqrt(-1) could be defined using the "new" value ln(-1). 

Yes, I did know that e^iπ = -1

Thanks for both of the replies, and I'll go away and have a ponder on this.

Thank you both.  The words "algebraically closed" tell me what I needed to know, but I hadn't made the leap that rules out 3D.  when I have some time to spare I think I had better look Quaternions up in Wiki and hope I can understand some of that.

random fruit

Perhaps in the time it takes you to refresh, the number of users goes down?  It's probable that the database system (MySQL) only has a user connected during the period the messages are being selected from the database.  This is only happening between a user clicking on a message title and the message text appearing on his/her screen. 

Amusing... when I pressed the 'submit' button for this post, I got the same message myself!

MySQL is the system (a database management system) which stores and organises the message texts of Maths is fun.  When designing an application of a database, it is desirable to have an allowed maximum number of uses at any one time.  The error message above says the system has already reached this limit, and so you can't connect.

Oops - I spotted Jane's contribution only when my post caused page 2 of the discussion to be displayed; until then I hadn't got as far as page 2.  Can I console myself that I had a similar idea to Jane?

I'd like to see the idea expressed by Paul Lockhart taken into English schools.  Every week I work with electricians who cannot recall Ohm's law (V = IR) and who cannot transpose it (I = V/R) and then who cannot use it to predict the current (I) given the voltage (V = 230) and a resistance (R = 0.35).  When I tell them to divide 230 by 0.35 they cannot operate the calculator in front of me to get the arithmetic result (go on, try for yourself... did you get 657?)  This matters for electrical safety! 

And so very often those who left school at 16 in England can't do this simple piece of maths, and think its nasty and evil and what they became an electrician to avoid.  If Paul Lockhard's approach will overcome this depressing mess, I'd think it wonderful, and I feel his point of view should be given a chance to make a difference.

Agreed, we Brits don't use American order of days and months.  But do you Yanks think we should celebrate 'e' month in Feb '71?  And if not, why not?

Be careful!  If the type of 'angle' is an integer, the real maths involved in the second example can result in a loss of accuracy.  What may be better for an integer, might be to take the value modulo 360.  Also, the first piece of code does nothing where the value of the angle is already less than zero.

One of my children (all now grown into sensible adults, but that's another story) finally understood percentages when I talked with her about it in terms of money.

First, one percent of one pound is one penny.  (This is £ sterling in UK, but applies just as well to Euros and cents, Dollars and cents, etc).

Second, a one percent increase applies to every pound of wages earned in a week.  So, for examples:
£1/week + 1% gives £1.01/week
£2/week + 1% gives £2.02/week
£1/week + 2% gives £1.02/week
£2/week + 2% gives £2.02/week
We discussed what percentage her pocket-money should go up next birthday in similar fashion.  She soon got the idea from the pattern above.

Finally we discussed reductions by a percentage.  At a sale in a shoe shop, some shoes were advertised as 25% off.  I said, it probably meant that those shoes now cost 75p for each £1 they used to cost before the sale.  We did some examples:
£1 gone down to 75p
£2 gone down to £1.50
£3 gone down to £2.25
£10 gone down to £7.50
£40 gone down to £30. 
On the last she said "Huh, I can tell how often you buy womens' shoes" but I protested "But Dads don't buy womens' shoes."

A few days later she followed up with:  Why did you say "it probably means"?  I joked that some shop-keepers with a particularly keen desire to emphasise the value-for-money of their goods, could compute the percent reduction another way.  I said, if a pair of shoes now cost £50 and used to cost £100, could that be computed as 100%?  She said "no" but I reminded here that the reduction (£100-£50) was £50 which was clearly reduction-in-price/original-price = £50/£50 and therefore 100%.  She said "that's cheating" and I said it was not beyond the guile of some.  I'd like to think that UK trading standards departments have an opinion about this, but I have no experience.

Finally, whenever I hear a percentage being mentioned on the news: "house prices in the UK have fallen 12% over the last year, says" I have three questions: (a) show me the input data (b) how do you justify the computations and (c) who wishes to prove what with it. 

In my opinion, percentages are often poorly understood by many people and this results in a mis-use of them as heresay and opinion, and not useful arithmetic.  I think it would be a good idea if only interest rates on loans and savings, and rates of tax, were expressed in percentages.

Hey, that's my education bit (and rant) over, hope some of you enjoyed it.

One that I was taught at a Electrician's class, consisting mostly of teenagers, for the sin, cos and tan:

gender Over Here Can Always Happen To Old Age

which means:
gender Over Here: Sin = Opp / Hypot
Can Always Happen: Cos = Adjac / Hypot
To Old Age: Tangent = Opp / Adjac