• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month
Page
1. 1
1
2. 2
2
3. 3
3
4. 4
4
5. 5
5
6. 6
6
7. 7
7
8. 8
8
9. 9
9
10. 10
10
11. 11
11
12. 12
12
13. 13
13

# I have been given the following equation to use to investigate Isoperimetric Quotients:-

Extracts from this document...

Introduction

I have been given the following equation to use to investigate Isoperimetric Quotients:-

I will begin by investigating the Isoperimetric Quotients of rectangles:-

Using this method I have gathered the following results:-

 Width (cm) Length (cm) IQ 2 5 0.641* 3 24 0.310 12 17 0.762 2 10 0.436 3 7 0.659 1 4 0.503** 3 3 0.785 2 6 0.589*** 1 3 0.589*** 12 3 0.503** 4 6 0.754 6 15 0.641*

At this stage I can observe that IQ’s of rectangles are all less than 1. I

Middle

This proves that rectangles in the same ratio have the same IQ.

In the table the rectangle with the largest IQ was a Square, and the lowest IQ was a long, thin rectangle. I will now look further into this, and to keep it fair, both shapes will have the same area:-

This is another long, thin rectangle and has a low IQ.

This square has a high IQ.

I can conclude from this that the higher the difference between the lengths and widths of the rectangle, the lower the IQ will be.

Returning to the earlier statement, that rectangles in the same ratio have the same IQ, I can conclude that we can only work out a general formula for squares:-

Summary of rectangles:-

All rectangles in the same ratio have the same IQ. This means we can only find the pattern for regular shapes. The larger the difference

Conclusion

I think this means that an Isoperimetric Quotient is a measurement of how efficiently a shape covers area, with a certain perimeter, or how it covers a certain area with as little perimeter as possible.

I will now investigate this, using a fixed perimeter of 80cm:-

Summary of fixed perimeter investigation:-

The square has the smallest IQ, and also holds the smallest amount of area. The circle has the largest IQ and holds the most area.

## CONCLUSION:-

The last investigation proves that IQ must be the measurement of how efficient a shape covers an area with a certain perimeter, or how little perimeter a shape will use to cover a certain area. The worst regular plane polygon is the triangle. There is a limit of 1 that only the circle reaches, and the number of sides a regular polygon has increases infinitely towards that limit. This is probably because as the number of sides increases, the shape becomes more efficient at containing an area.

This student written piece of work is one of many that can be found in our GCSE Height and Weight of Pupils and other Mayfield High School investigations section.

## Found what you're looking for?

• Start learning 29% faster today
• 150,000+ documents available
• Just £6.99 a month

Not the one? Search for your essay title...
• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month

# Related GCSE Height and Weight of Pupils and other Mayfield High School investigations essays

1. ## Liquid chromatography is a technique used to separate components of a mixture to isolate ...

before decreasing by ~7% between 1 in 10 and 1 in 5 dilutions. A large decrease in % efficiency is evident between 1 in 5 and the standard of ~48%. It could be suggested that the column starts to become overloaded with all three compounds between the 1 in 10 and 1 in 5 dilutions by analysing these results.

2. ## Is there a link between IQ and Key Stage 2 results?

I have decided to do this so that it shall be easier to compare the two gender groups and to notice any connections or patterns. I shall create histograms to compare the number of grades attained by each group. I shall also use Pie charts to compare the different grades attained in proportion with the total for each group.

1. ## Is race and intelligence a justifiable area of research in psychology?

scientific fraud, produced the data for a large proportion of twin studies. Nevertheless even if these figures are accepted, they are misleading. The results cannot be used in generalising to populations, as the small sample is unrepresentative of the whole population i.e.

2. ## Compare the connection between weight and hours spent watching TV, and IQ and TV ...

Assuming that the interviewer is friendly, this is likely to be quite high. Disadvantages - * Expense - the procedure uses up a lot of time for each interviewer. There may also be costs associated with the travelling between respondents.

1. ## Investigation on the shape and size of limpets on a sheltered rocky shore called ...

However all other variables such as the type of limpet, need to be kept constant. I have chosen a sheltered shore called Frenchman's Steps in Wales to carry out my experiment. I have chosen to measure the height and width of limpets at 2 different heights on the shore this is the variable which I will change.

2. ## Investigation into the shapes of limpets on sheltered and exposed rocky shores.

Finally, the lowest zone, known as the sublittoral zone, extends below water and its upper limit is marked by the presence of large seaweeds or algae. On an exposed rocky shore the upper limit of each zone is extended vertically due to increased wave action and heavy winds carrying spray further up the shore.

• Over 160,000 pieces
of student written work
• Annotated by
experienced teachers
• Ideas and feedback to