Maths question

[wee quinnie]

Hi All,

Can someone help me explain this to my Mathematically challenged friend? The only thing I have been able to come up with by way of explanation is that this is the difference between addition and multiplication.

Email from my friend:

My maths abilities are beginning to concern me a bit. There is quite a bit of maths in the PGCE. Lk was trying to explain to me how perimeters work the other day. She can't understand where this is a problem for me. So do you get this? Here is what is going on in my head. Supposing I took leave of my senses and wanted to lay a patio. I went out and bought the tiles for the floor area and fencing panels to contain it. The patio was 6 metres by 12 metres. That is an area of 72 metres. That requires 36 metres of fencing. But, wife doesn't like the shape. She wants a bigger patio and that one is 8 metres by 10. That is an area of 80 metres. I have to go out and buy more tiles because the area is bigger. Yet amazingly it doesn't require more fencing to contain it. That does not make sense. It is a bigger area. It takes up more space. To contain it should require more fencing. Yet it doesn't. My brain cannot understand how this can possibly be the case. So even though C devised the handbag strap demonstration it still makes no sense. It is like witnessing an optical illusion.

[Tony.London Suburbs]

The second patio is nearer to a square making more efficient use of the perimetre of the fencing.

As you get nearer to a square the area gets bigger for any length of fencing and if you use 9 metre square patio you would use still use 36 metres of fence but you would have 81 square metres of tiles(9x9)...

The ideal use of a perimetre is a circle,if you arranged the 36 metres of perimetre into a circle that would be the biggest usage of the area possible.

[HonaloochieB]

Ladies and gentlemen, a big hand please for the mathematic stylings of WQ and TLS and their wry sideways glance at patios.

They're here all week, at least, and you can be sure they'll be taking requests.

Remember they know to the centimetre how much distance your waitress covered to serve you, so please be good to her.

Drive safely now.

[Tony.London Suburbs]

I'll just answer one request from a regular reader and contributor:

Dear TLS: OK I am trying to figure out home much cubic litres my intercooler and intercooler piping are, I have the length of ic piping, the size of the tubing, I just need the equation to figure it out.

I also have the measurements of the core and such of the IC, that I can figure out pretty easy just have to convert that from sq inches to litres.?

Can you help please?

TLS Says: Cylinder volume = 3.1416 * (Radius^2) * Length ....

Over to much more important and pressing matters...how will said waitress serve me,exactly Hona?:)

[HonaloochieB]

She'll serve you good and proper TLS, or I for one will want to know why not, if not.

Ladies and gentlemen, it's equations. it's intercooler piping

IT'S THE ONE AND ONLY TLS!!!!

[SimonM]

I am intrigued by this concept of the "cubic litre" myself....

PS Do I get to choose my waitress? :))

[Tony.London Suburbs]

HonaloochieB Wrote:

She'll serve you good and proper TLS, or I for one will want to know why not, if not.

Ladies and gentlemen, it's equations. it's intercooler piping....

The equation ?...Waitress + Service = Immense satisfaction for my Intercooler Piping System:))

[Tony.London Suburbs]

Hona! Can you arrange for the waitress to make a return visit,pretty please?B)

[giggirl]

Dearest Wee Quinnie,

I tried so very hard to get to grips with your patio conundrum but I got bored just reading the measurements and gave up. It was dull (sorry). I?m the first to admit that a very expensive education was wasted on me and that my mathematical abilities are alarmingly bad. The sums get a tad more accurate when a ? sign is inserted first, but I?m still not going to be winning any prizes.

My advice to your mathematically challenged friend is to go to Iceland. The pricing structure is so easy-peasy; you arrive at the till knowing exactly what your final bill will be. I?ve been going to Iceland for three weeks now and I feel like Stephen Hawkins. The girl on the till says ?that will be ?8 madam? and I shout back at her ?yes I know ? isn?t it wonderful??. But there again I?ve not been getting out much recently.

I hope this helps.

[Huguenot]

We can get just crazy with the amount of fencing, and it should be a lesson to all of us with long thin gardens.

The original patio was 6m x 12m - 72sqm and 36m of fencing. Imagine if this was made out of 72 1mx1m tiles, and instead of lying them in a 6m x 12m block, they were laid end to end, resulting in a strip 72m long, 1 m wide, and 146m of fencing!!

God forbid they were made out of 10cm tiles. Laid end to end it would 720m long, 10cm wide, and 1.46 km of fencing.

Use those 1cm mosaic tiles, and you could achieve a patio 7.2km long, 1 cm wide requiring 14.402 km of fencing.

They'd all be the same surface area of course (72sqm)

Outrageous. It's a plot by the Victorians you know.

[Tony.London Suburbs]

Huguenot Wrote:

We can get just crazy with the amount of fencing,

.... Outrageous. It's a plot by the Victorians you know.

There's a perfect example of this in Hanover Square in Central London.

[bignumber5]

(edited as post seemed to come out twice)

[bignumber5]

For squares and rectangles, Area is one side multiplied by the other, Perimeter is adding all 4 sides together.

6 by 12

Area = 6x12 = 72

Perimeter = 6+12+6+12 = 36

8 by 10

Area = 8x10 = 80

Perimeter = 8+10+8+10 = 36

So if using 1x1 tiles/slabs and a roll of fencing, you need 8 more tiles but the fencing roll will still be long enough.

Make Sense?

[wee quinnie]

bignumber5 Wrote:

-------------------------------------------------------

> For squares and rectangles, Area is one side

> multiplied by the other, Perimeter is adding all 4

> sides together.

>

> 6 by 12

> Area = 6x12 = 72

> Perimeter = 6+12+6+12 = 36

>

> 8 by 10

> Area = 8x10 = 80

> Perimeter = 8+10+8+10 = 36

>

> So if using 1x1 tiles/slabs and a roll of fencing,

> you need 8 more tiles but the fencing roll will

> still be long enough.

>

> Make Sense?

Thanks for that BN5 - HOWEVER the question is really about why do perimeters remain the same, even if areas increase.

[wee quinnie]

giggirl Wrote:

-------------------------------------------------------

> Dearest Wee Quinnie,

>

> I tried so very hard to get to grips with your

> patio conundrum but I got bored just reading the

> measurements and gave up. It was dull (sorry).

> I?m the first to admit that a very expensive

> education was wasted on me and that my

> mathematical abilities are alarmingly bad. The

> sums get a tad more accurate when a ? sign is

> inserted first, but I?m still not going to be

> winning any prizes.

>

Giggirl - I hear ya! I know what you mean, and you are right, but my wee friend Mark is getting in such a state about this, and he is not hearing my explanation, which i will summarise as "that's the difference between multiplication and addition". I am contemplating starting a thread about shoes though. That is probably quite boring but in a different direction.

[giggirl]

Oh please please do start a thread about shoes. I cannot think of anything more thrilling. I have an addiction don't you know? And there's no 12 step programme which covers shoes - I've checked. I'm to be pitied really.

[Tony.London Suburbs]

The second patio is nearer to a square making more efficient use of the perimetre of the fencing.

As you get nearer to a square the area gets bigger for any length of fencing and if you use 9 metre square patio you would use still use 36 metres of fence but you would have 81 square metres of tiles(9x9)...

The ideal use of a perimetre is a circle,if you arranged the 36 metres of perimetre into a circle that would be the biggest usage of the area possible.

In case that previous post is invisible,there's your answer which you have not even acknowledged..

[LuvPeckham]

Read this with increasing fascination and as a result have now just slit my wrists ......(it's a lot less painful and quicker then going on with this discussion)

[bignumber5]

Thanks for that BN5 - HOWEVER the question is really about why do perimeters remain the same, even if areas increase.

Coincidence of the numbers in question, because you upped the dimensions of one side by the same amount that you dropped the other side by. Doing this makes a difference to the area (because it is based on multiplication) but the perimeter remains constant (because it is based on addition). The "but why?" question can only really be answered with a smidge of basic algebra. Have put it below, but realise that if your freind is a bit baffled by the mathematics of this then it may not help:

If the first rectangle has sides A by B metres (in your example, A=12, B=6)

Area = AxB = AB sq.metres

Perimeter = A+B+A+B = 2A + 2B = 2(A+B ) metres

Now the second rectangle has measurements (A-2) by (B+2) metres

Area = (A-2)x(B+2) = AB + 2A - 2B - 4 sq.metres

Perimeter = (A-2)+(B+2)+(A-2)+(B+2) = 2A + 2B = 2(A+B ) metres

So if you change the sides by equal and opposite amounts (ie +2 to one and -2 to the other in your example) the area will change but the perimeter will not. If you change them by unequal amounts, the perimeter will vary.

I hope this makes it clear.

[indiepanda]

Or if the algebra doesn't work, try trying a piece of string/wool/cotton in a loop and just see the difference in the area inside based on how you hold it.

Put a finger in each end and hold it tight and you get the long skinny garden without much inside - spread it out on a piece of paper so it looks like a circle and suddenly lots more space inside - the more rectangular version is closer to the long skinny and the squarer version is closer to the circle.

[Tony.London Suburbs]

indiepanda Wrote:

Put a finger in each end and hold it tight and you get the long skinny garden without much inside spread it out on a piece of paper so it looks like a circle and suddenly lots more space inside - the more rectangular version is closer to the long

skinny and the squarer version is closer to the circle.

Indedy Indie:))The ideal use of a perimetre is a circle,if you arranged the 36 metres of perimetre into a circle that would be the biggest usage of the area possible

[indiepanda]

I know. Might want to try with a piece of string not to scale of course!

[LuvPeckham]

SIGH

You lot are so 2 Dimensional

Has no one considered the height of the fence in this and if you get a tall fence but then cut it down in size can you then use the resultant additional bits of fencing to cover more of the perimeter ?

Come on people think outside of the box on this one....

However if Train A is travelling at 50 miles per hour and a Car is on a right angle interception point doing 32 miles per hour, the train is 125 miles from the crossing and the car is 81.9 miles from the crossing will the car clear the crossing before or after the train ... now this one also needs you to know how long the train is .....

(Remember Children it is never safe to cross a level crossing when the barrier is down, however as there are no level crossings in East Dulwich ...)

[Jeremy]

indiepanda's explanation is good... should make it clear to the slowest of maths brains. You should be a teacher!

[HonaloochieB]

giggirl Wrote:

-------------------------------------------------------

> Oh please please do start a thread about shoes. I

> cannot think of anything more thrilling. I have

> an addiction don't you know? And there's no 12

> step programme which covers shoes - I've checked.

> I'm to be pitied really.

Have you got shoes you've bought and never worn?

My first admission is the mustard ostritch skin chisel-toed beauties.