Posts Tagged ‘radius’

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The Rolling Coin Paradox that drove me Crazy!

February 27, 2026

Consider the example of the coin rolling around a coin of the same size. Intuitively we think …’OK. Same circumference, so the coin will rotate once as it rolls around a same-size coin. But this doesn’t happen. It rotates twice.

TWICE!

This observation is SOOOOOOOO counterintuitive we have to know why?

Why?

The answer is interesting. The relevant point in the ROLLING COIN PARADOX is the centre of the rolling coin. The rolling coin rotates about that point. And that centre (the red dot in the gif below) moves through a circle twice the circumference of the stationary coin. It is much easier to understand when you see it. (Below)

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The Rolling Coin Paradox that drove me Crazy!

June 4, 2020

The MindYourDecisions blog (Video below) presents the PARADOX beautifully. 

Now consider the example of the coin rolling around a coin of the same size. Intuitively we think …’OK. Same circumference, so the coin will rotate once as it rolls around a same-size coin. But this doesn’t happen. It rotates twice.

TWICE!

This observation is SOOOOOOOO counterintuitive we have to know why?

Why?

Mr. MindYourDecisions doesn’t explain why this happens. The answer is interesting. The relevant point in the ROLLING COIN PARADOX is the centre of the rolling coin. The rolling coin rotates about that point. And that centre (the red dot in the gif below) moves through a circle twice the circumference of the stationary coin. It is much easier to understand when you see it. (Below)

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Sharp Shooter Maths …. METRIC

May 10, 2019

Mathspig grew up on a police station in the small Australian country town of Kyneton, Victoria in the 1960s. Australia has a very strict gun laws today. But such laws didn’t exist in the sixties. My Dad’s .22 rifle rested against our fridge. He pocketed the magazine.

A .22 means a bullet calibre of .22 inches.

My Dad the Sharp Shooter stopped a stolen car with one bullet. This was considered legendary by his fellow cops. He didn’t shoot the tyres. He managed, by accident and possibly even though he was aiming at the tyres, to hit the electrical lead into the car’s  distributor cap. Phht! Car go no more. More on my childhood here.

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Sharp Shooter Maths

One measure of the accuracy of rifles, riflescopes but also the sharpshooter is the MOA or Minute of Angle.  The MOA can also be used to define the target zone (circle).

I cannot show you a triangle with an angle of 1′ because it would have to be 100m long on one side and only 3cm tall.

Needless to say, drawings are NOT to scale.

A sharpshooter can put 5 out of 6 bullets in a target zone drawn at 1′ angle around centre of target at any distance.

As the distance away from the target increases the target zone circle area increases.

A sharp shooter would be considered very skilled if they can shoot within a target zone (circle) of 10.5 inch radius at 1000 yds. Hitting a bull’s eye at this distance is down to luck.

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Sharp Shooter Math …. USA units

May 8, 2019

Mathspig grew up on a police station in the small Australian country town of Kyneton, Victoria in the 1960s. Australia has a very strict gun laws today. But such laws didn’t exist in the sixties. My Dad’s .22 rifle rested against our fridge. He pocketed the magazine.

A .22 means a bullet calibre of .22 inches.

My Dad the Sharp Shooter stopped a stolen car with one bullet. This was considered legendary by his fellow cops. He didn’t shoot the tyres. He managed, by accident and possibly even though he was aiming at the tyres, to hit the electrical lead into the car’s  distributor cap. Phht! Car go no more. More on my childhood here.

cc

cc

Sharp Shooter Maths

One measure of the accuracy of rifles, riflescopes but also the sharpshooter is the MOA or Minute of Angle.  TheMOA can also be used to define the target zone (circle).

I cannot show you a triangle with an angle of 1′ because it would have to be 100 yds long on one side and only 1 inch tall.

Needless to say, drawings are NOT to scale.

A sharpshooter can put 5 out of 6 bullets in a target zone drawn at 1′ angle around centre of target at any distance.

As the distance away from the target increases the target zone circle area increases.


A sharp shooter would be considered very skilled if they can shoot within a target zone (circle) of 10.5 inch radius at 1000 yds. Hitting a bull’s eye at this distance is down to luck.

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MATH JOKE 7: Bubble Gum

January 21, 2019