Maths buffs out there, please give us a clue or revision about how this pi wheel works. I gave everything back to the teacher a long time ago.

All I know now is how to divide a piece of cake into equal portions to share with the number of people in the room or cut bigger portions for the big eater.

Ngai C O says:

Hi,

On the Database, there are 4 pictures
Picture 1 – Wooden Segmented Pi circle
Picture 2 – Wooden Quadrilateral Shapes
Picture 3 – Wooden Rectangular Prism
Picture 4 – Wooden 5 sided shape without English
description (obviously an irregular
pentagon)
Estimated year and location – 1940/Ipoh.

I am beginning to realise that I have not lost it all and am recalling the geometry, trigonometry, algebra etc that I learned. Problem was it got rusty due to non regular usage. All I need is some revision and most of the knowledge would doubtless return with a much better understanding of the different concepts.

Remember that in our time, learning was mainly by rote and memorisation as dictated by the teacher. Half the time, we only answered correctly because of the memorisation.

The recent and current trend is learning by exploration and research, which takes one to understand the concept of a problem much better.

The Chinese method at the time was largely rote learning. The was and is true of learning the Chinese language. I might be wrong as there may well be another method adopted.

Ngai C O says:

Hi,

I like to add that the word ‘prism’ was used to describe the rectangle.

I hope people can tell the difference that prism means something else.

This differentiation is so important to today’s students, where unfortunately a certain standard has dropped as the recent headline tourism notice demonstrated.

Ngai C O says:

Hi,

Whilst I have this momentum to write a bit more about the Teaching Aid, I shall capitalise on it. ( By the way, I am also waiting for my home made Bak Kwa or jerk pork to cook in the oven in the meantime; just in time for the Chinese New Year. The recipe from a Monday to Friday Ipoh Blogger. Thank You.)

We used a Helix or similar instrument set to draw up the shapes and angles as required compared to the Teaching Aid. I suppose the Chinese School students used the similar Helix set. I believe this is still being used.

Today with computer aided designs or CAD and software, people are fortunate to get the problems solved in no time with all the apps. available. Mostly typing in the main parameters and various options would show up. This was how I did my brief revision if people want to know. It is so quick and easy. In the old days, if one did not have one the at hand, one had to physically visit a friend or the library or the bookshop. We would be lucky to have a phone to call someone. If we had one the other party might not. Still, we got by somehow without moaning and getting frustrated.

However, imagine our mobile phones crack up and our internet dies, we would be in a fit.

Ipoh Remembered says:

Dear Ngai C O …

how this pi wheel works.

You can use it to calculate a rough value of π using only a ruler (and maybe a little arithmetic). The rough calculation works because a regular polygon approaches a circle if it has sufficiently many sides.

First, ignoring the wheel, consider a perfect circle with circumference C and radius r:

C = 2πr ∴ π = C/2r

If, instead of a perfect circle, we have a regular polygon inscribed in a circle, then the more sides the polygon has, the closer its perimeter approaches the circumference of the circle. (A hexagon is more “circular” than a pentagon; a dodecagon even more “circular”; and so on.)

Now, the wooden model: Fully assembled, it’s a many-sided polygon, so it’s not a perfect circle but it’s close. Each triangular piece of wood has two long edges and one short one. Each long edge can be seen as the radius of the polygon; and all the short edges, taken together, are the perimeter, which approximates a circle.

Suppose the long edge of each piece measures 0.5 (metres, feet, it does not matter). Then if you measure the lengths of all the short edges and add them up, the total should be a reasonable estimate of π.

Ngai C O says:

Hi Ipoh Remembered,

Thanks. I think I got it. The outer sides form a 60 sixty sided polygon, called hexacontagon. There are 60 triangular segments of that make up the sphere.

Ngai C O says:

Hi Ipoh Remembered,

Question. Why is a sixty sided polygon chosen as teaching aid? Why not 61 sided or 72 sided?

Ipoh Remembered says:

Well, I don’t know why 60 was chosen. (Was it? Did you count? I was too lazy!)

The more pieces the better for estimating π — but on the other hand, the more pieces the more fragile each piece is at the sharper end.

And why not 61? Perhaps because 360/61 would be more difficult to measure and cut, without adding much accuracy to the estimate of π.

I’m guessing.

Happy New Year, by the way.

Ngai C O says:

Hi Ipoh Remembered,

Happy New Year.

Sorry if I asked too much from you.

Yes, I counted 60 pieces.

felicia says:

Thank you for the short Maths lesson, Ipoh Remembered & Ngai!
As for “why 60 was chosen”…similar to what Ipoh Remembered said, maybe because it’s easier to calculate; easier to divide 360 with an even number perhaps?

Ngai C O says:

Hi felicia

Of course, I was pushing my luck because it would end up with many decimals.

Ipoh Remembered says:

Dear Ngai C O …

unfortunately a certain standard has dropped as the recent headline tourism notice demonstrated.

Can you elaborate? I don’t understand the reference.

Ngai C O says:

Hi Ipoh Remembered

If you go to Channel NewsAsia dated 18/01/2018, titled Error Ridden Notice posted by the Perak Tourism Dept, it will show you what I mean.

Sorry I have to make you work for it. I suppose a little more finger exercise is good for the circulation.

Ipoh Remembered says:

Thanks. I looked it up — it was a bit painful to read — but then I found the following note:

The Ipoh City Council said it will take action against the person responsible for the notice.

Of course they will not take action against the politicians and bureaucrats who are responsible for the state of language education.

It’s so much easier just to blame a low-ranking person.

Ipoh Remembered says:

Dear felicia … Can you give us some idea of the size of the circle? Even just an estimate of the box size will do. Thanks.

## Ngai C O says:

Hi,

Maths buffs out there, please give us a clue or revision about how this pi wheel works. I gave everything back to the teacher a long time ago.

All I know now is how to divide a piece of cake into equal portions to share with the number of people in the room or cut bigger portions for the big eater.

## Ngai C O says:

Hi,

On the Database, there are 4 pictures

Picture 1 – Wooden Segmented Pi circle

Picture 2 – Wooden Quadrilateral Shapes

Picture 3 – Wooden Rectangular Prism

Picture 4 – Wooden 5 sided shape without English

description (obviously an irregular

pentagon)

Estimated year and location – 1940/Ipoh.

I am beginning to realise that I have not lost it all and am recalling the geometry, trigonometry, algebra etc that I learned. Problem was it got rusty due to non regular usage. All I need is some revision and most of the knowledge would doubtless return with a much better understanding of the different concepts.

Remember that in our time, learning was mainly by rote and memorisation as dictated by the teacher. Half the time, we only answered correctly because of the memorisation.

The recent and current trend is learning by exploration and research, which takes one to understand the concept of a problem much better.

The Chinese method at the time was largely rote learning. The was and is true of learning the Chinese language. I might be wrong as there may well be another method adopted.

## Ngai C O says:

Hi,

I like to add that the word ‘prism’ was used to describe the rectangle.

I hope people can tell the difference that prism means something else.

This differentiation is so important to today’s students, where unfortunately a certain standard has dropped as the recent headline tourism notice demonstrated.

## Ngai C O says:

Hi,

Whilst I have this momentum to write a bit more about the Teaching Aid, I shall capitalise on it. ( By the way, I am also waiting for my home made Bak Kwa or jerk pork to cook in the oven in the meantime; just in time for the Chinese New Year. The recipe from a Monday to Friday Ipoh Blogger. Thank You.)

We used a Helix or similar instrument set to draw up the shapes and angles as required compared to the Teaching Aid. I suppose the Chinese School students used the similar Helix set. I believe this is still being used.

Today with computer aided designs or CAD and software, people are fortunate to get the problems solved in no time with all the apps. available. Mostly typing in the main parameters and various options would show up. This was how I did my brief revision if people want to know. It is so quick and easy. In the old days, if one did not have one the at hand, one had to physically visit a friend or the library or the bookshop. We would be lucky to have a phone to call someone. If we had one the other party might not. Still, we got by somehow without moaning and getting frustrated.

However, imagine our mobile phones crack up and our internet dies, we would be in a fit.

## Ipoh Remembered says:

Dear

Ngai C O…You can use it to calculate a rough value of π using only a ruler (and maybe a little arithmetic). The rough calculation works because a regular polygon approaches a circle if it has sufficiently many sides.

First, ignoring the wheel, consider a

perfect circlewith circumference C and radius r:C = 2πr ∴ π = C/2r

If, instead of a perfect circle, we have a regular polygon inscribed in a circle, then the more sides the polygon has, the closer its perimeter approaches the circumference of the circle. (A hexagon is more “circular” than a pentagon; a dodecagon even more “circular”; and so on.)

Now, the wooden model: Fully assembled, it’s a many-sided polygon, so it’s not a perfect circle but it’s close. Each triangular piece of wood has two long edges and one short one. Each long edge can be seen as the radius of the polygon; and all the short edges, taken together, are the perimeter, which approximates a circle.

Suppose the long edge of each piece measures 0.5 (metres, feet, it does not matter). Then if you measure the lengths of all the short edges and add them up, the total should be a reasonable estimate of π.

## Ngai C O says:

Hi Ipoh Remembered,

Thanks. I think I got it. The outer sides form a 60 sixty sided polygon, called hexacontagon. There are 60 triangular segments of that make up the sphere.

## Ngai C O says:

Hi Ipoh Remembered,

Question. Why is a sixty sided polygon chosen as teaching aid? Why not 61 sided or 72 sided?

## Ipoh Remembered says:

Well, I don’t know why 60 was chosen. (Was it? Did you count? I was too lazy!)

The more pieces the better for estimating π — but on the other hand, the more pieces the more fragile each piece is at the sharper end.

And why not 61? Perhaps because 360/61 would be more difficult to measure and cut, without adding much accuracy to the estimate of π.

I’m guessing.

Happy New Year, by the way.

## Ngai C O says:

Hi Ipoh Remembered,

Happy New Year.

Sorry if I asked too much from you.

Yes, I counted 60 pieces.

## felicia says:

Thank you for the short Maths lesson, Ipoh Remembered & Ngai!

As for “why 60 was chosen”…similar to what Ipoh Remembered said, maybe because it’s easier to calculate; easier to divide 360 with an even number perhaps?

## Ngai C O says:

Hi felicia

Of course, I was pushing my luck because it would end up with many decimals.

## Ipoh Remembered says:

Dear

Ngai C O…Can you elaborate? I don’t understand the reference.

## Ngai C O says:

Hi Ipoh Remembered

If you go to Channel NewsAsia dated 18/01/2018, titled Error Ridden Notice posted by the Perak Tourism Dept, it will show you what I mean.

Sorry I have to make you work for it. I suppose a little more finger exercise is good for the circulation.

## Ipoh Remembered says:

Thanks. I looked it up — it was a bit painful to read — but then I found the following note:

Of course they will not take action against the politicians and bureaucrats who are responsible for the state of language education.

It’s so much easier just to blame a low-ranking person.

## Ipoh Remembered says:

Dear

felicia… Can you give us some idea of the size of the circle? Even just an estimate of the box size will do. Thanks.