Jump to content

Random maths

davenportram

By davenportram
in The Jim Smith Room

Recommended Posts

  • Replies 197
  • Created
  • Last Reply
blackNwhites

blackNwhites

Posted
Posted

http://upload.wikimedia.org/wikipedia/commons/thumb/b/b8/999_Perspective/800px-999_Perspectivehttp://en.wikipedia.org/wiki/0.999...

The equality 0.999... = 1 has long been accepted by mathematicians and is part of general mathematical education. Nonetheless, some students find it sufficiently [url=http://en.wikipedia.org/wiki/Counterintuitive]counterintuitive that they question or reject it, commonly enough that the difficulty of convincing them of the validity of this identity has been the subject of several studies in mathematics education.
Link to comment
Share on other sites
Martyn

Martyn

Posted
Posted

Yeah, it's hard to put it in simple terms... How about this:

When you have the number 0.999... and the number 1, for there to be a difference between the two there has to be a number between them...

[snip]

Hopefully that's understandable.

Having an interest in mathematics this is something I "know" even though my "head" hasn't always gotten it. And even though it doesn't to have worked for anyone else, your explanation is the best I've heard and I've think I've got it at last! 'http://www.dcfcfans.co.uk/public/style_emoticons/<#EMO_DIR#>/smile' class='bbc_emoticon' alt=':)' />

Thanks Albert!

Link to comment
Share on other sites
ladyram

ladyram

Posted
Posted

Have to say, I don't do maths, but that^^, is fascinating. Maths in nature, more specifically spirals in nature - who'd have thought it? Not me.

Link to comment
Share on other sites
  • 3 weeks later...
Albert

Albert

Posted
Posted

Have you ever sat there and thought: "I wonder what day of the week March the 3rd 1847 was?" and not had a computer or any other way of finding out? Well, here's a method that can allow you to figure out what day it was quickly:

Take your year and split it up into how many hundreds of years, so for 1847 it would be 18, and then use how many years into your century you are, so in this case 47.

1. Now take your years into the century and divide them by 12, round down:

47/12 = 3.916...

So this rounds down to 3.

2. Then find the remainder from this previous divison:

In this case since 3*12 is 36 we'll get 47-36 = 11.

3. Finally, take the above number and divide it by 4, rounding down:

For example, 11/4 = 2.75, so 2.

4. Add all these numbers together:

Here this would be 3+11+2 = 16

5. Now add another number for the century the year is in. For the 1800s (so 18 for these purposes, it's the 19th century for naming purposes) it's 5, for the 1900s it's 3, for the 2000s, it's 2 and for the 2100s it'll be 0:

For example, since it's the 1800s for this example it'll be 16+5 = 21.

6. Now we take the modulo of this number in 7, this being because the week has 7 days. Basically, think of a clock and how even after 21 hours pass after 1, it's 10, not 22. The number wraps around. Another way is finding the remainder of the number you find divided by 7.

In this case, it's 0.

This gives you the "doomsday" for the year. Knowing this day you can figure out what day of the week any date is. This date will correspond to (in day/month format):

3/1 or 4/1 for leap years

28/2 or 29/2 for leap years

7/3 or 0/3 (so the last day of February)

4/4

5/9

6/6

7/11

8/8

9/5

10/10

11/7

12/12

To remember these, basically for even months it's the same as the month's themselves except for February. For the odds, remember 7-11 and 5 to 9, as these work for both (for example, 5/9, 9/5, 11/7 and 7/11). Also remember the last day of February and the 3rd or 4th of January depending of whether it's a leap year.

What did that number before mean though? The zero that was found?

Well, the number corresponds to the day of the week, here are what they are below:

0: Sunday

1: Monday

2: Tuesday

3: Wednesday

4: Thursday

5: Friday

6: Saturday

So we found that the doomsday was a Sunday.

So now we know that the doomsdays are Sundays that year. We need to know what 3rd of March was though. Well, we know that 1847 wasn't a leap year so the 28th of February (think, 0th of March) was a doomsday and as such a Sunday. As such 3 days later (the 3rd of March 1847) would be a Wednesday.

Yay! It's know as the doomsday rule or doomsday algorithm. If you learn it you can look like you have little to know life and bore your friends and family.

Coming up next, Rubiks Cubes or how to count to 1023 on your fingers... How far will you go to alienate those around you?

Link to comment
Share on other sites
Albert

Albert

Posted
Posted

True enough, impressive skills once again Albert.

It's hardly impressive. I assure you that given a couple of hours over the next week or so you could do this like a pro.

Do you know how binary works? If so, binary hands is hardly a real step. I enjoy it and it's something most people find impressive. Even only knowing only the basic method and the basic numbers it's actually surprisingly easy.

Link to comment
Share on other sites
blackNwhites

blackNwhites

Posted
Posted

It's hardly impressive. I assure you that given a couple of hours over the next week or so you could do this like a pro.

Do you know how binary works? If so, binary hands is hardly a real step. I enjoy it and it's something most people find impressive. Even only knowing only the basic method and the basic numbers it's actually surprisingly easy.

It's impressive to me. You're a quantom thingymajig!

Just reading a guide (for binary) now, interesting!

2 to the power of x = x (2^x)

I could probably work those out.

2 to the power of 1 = 2 (2^1)

2 = 4 (2^2)

3 = 8 (2^3)

etc..

011 = 12.

0101 = 20 etc..

Link to comment
Share on other sites
davenportram

davenportram

Posted
  • Author
Posted

Just reading a guide (for binary) now, interesting!

2 to the power of x = x (2^x)

I could probably work those out.

2 to the power of 1 = 2 (2^1)

2 = 4 (2^2)

3 = 8 (2^3)

etc..

011 = 12.

0101 = 20 etc..

You missed 2^0=1 and binary counts powers of two moving to the left not right.

So 011 would be 0x2^2 + 1x2^1 + 1x2^0 = 0+2+1 = 3

Binary is easier if you think place value. The column on the right is 1 then as you go left it doubled every time

1 = 1

11 = 1 + 2= 3

10 = 2

Link to comment
Share on other sites
Albert

Albert

Posted
Posted

Well, using your hands to count to 1023 is takes a little practice but can be useful.

The concept is fairly simple, picture your fingers as representing either a 0 (down) or 1 (up) and use that as a number.

Hold your fingers up and think of your leftmost as the starting point (or the rightmost if you prefer).

1: 10000:00000

2: 01000:00000

3: 11000:00000

4: 00100:00000

5: 10100:00000

6: 01100:00000

7: 11100:00000

8: 00010:00000

The general rule is basically:

1. To add one add one to the leftmost place

2. If the leftmost place is already at one, make it into a 0

3. If the above is replacing a one, add one to the next place

4. If adding another one, and the next position is a one, then make it a zero and add one to the next place

5. Repeat the above

At the end add up the fingers as follows:

1 2 4 8 16 : 32 64 128 256 512

Add up the number you get times the above. For example:

10111:10110

1+4+8+16+32+128+256 = 445

This can of course lead to unfortunate combinations. 132 for example...

Link to comment
Share on other sites

Archived

This topic is now archived and is closed to further replies.

Go to topic listing
×
×
  • Create New...