You Won’t Believe This Amazing Formula

[This is a back-issue of one of this site’s newsletters]

If you’ve been reading for a while, you might remember this puzzle: Can you find a rectangle whose area equals its perimeter?

For example, a 6 x 3 rectangle has a perimeter of 18 units, and the area is 18 square units. The same number!

Continue reading You Won’t Believe This Amazing Formula

Monday Morning Movies

[This is a back-issue from this site’s newsletters]

 

Next week I’ll have a nice math video to show you. In the meantime, here’s the plot synopses of a number of popular films. Can you guess which movie each one is?

Continue reading Monday Morning Movies

Old Game Now New

[This is a back-issue of this site’s newsletter]

Monday Morning Math is late this week, but for a good reason – I was rushing to finish the new version of my online traffic jam game! Continue reading Old Game Now New

Math and Medicine

 

This question was posed to a group of medical professionals.

A woman is tested for a particular type of cancer, and the test is positive. Worried, she asks how likely it is that she really has cancer. Which of these is the best answer?

Continue reading Math and Medicine

Football Fever!

[This is a back-issue of one of this site’s newsletters]

Remember Paul the Octopus?

Paul the Octopus sadly passed away on 26 October 2010, at the ripe old age of 33 months, but not before shooting to fame for his successful predictions of matches in the 2010 FIFA World Cup.

Continue reading Football Fever!

Heptagons, and the politics of 19th century France.

[This is a back-issue of one of this site’s newsletters]

When I was in junior high school, my math teacher was teaching us about ruler-and-compass constructions. Do they still teach this to kids? Anyway, he’d taught us how to construct certain shapes, then informed us – the heptagon, or regular seven-sided polygon, can’t be constructed using a ruler and compass.

Continue reading Heptagons, and the politics of 19th century France.

Rubik’s Cubes

[This is a back-issue of one of this site’s newsletters]

As Google may have already told you, this week marks the 40th anniversary of invention of Erno Rubik’s famous cube.

Many people find the cube horribly difficult to solve. If you’re one of those people, take heart in this or this.

Continue reading Rubik’s Cubes

Squares And Infinities

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So, President was being briefed by his Chiefs Of
Staff on the latest conflict. He listened, asked questions, hummed and
ahed. Then he asked “were there any casualties?”

The Defense Chief nodded. “Three Brazilian soldiers were killed”

“Oh my God.” said the President. He clutched the edge of his desk. A
tear appeared at the edge of his eye. “My God.”

The Chiefs glanced at one another, unsure how to respond to the
President’s obvious grief. Finally he looked up.

“How many millions in a brazillion?”

Oh-kay… not sure where that one came from. Ahem.

So, I got my computer to make a video, showing how to construct a
square with a ruler and a compass. You can see it here

.

Back to big numbers. A number of years ago, I ran a Big Numbers
Contest through my website. Kids had to come up with the biggest
number they could

write in a two inch by four inch box. You’d think that out of the
infinity of numbers, there’d be a clear winner. Astoundingly, the
competition ended in a draw

.

The rules said kids couldn’t write “Infinity”. The obvious reason is
that that would make the contest too easy. The real reason is that
“Infinity” isn’t a well-defined number. There are actually different
sizes of infinity.

Some of the paradoxes of infinity were made clear to me by a short
story by Stanislaw Lem, in this book

. I read it a long time ago. You may find similar presentations by
googling Hilbert’s Hotel Paradox.

Yours,

Michael Hartley


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So, President was being briefed by his Chiefs Of Staff on the latest conflict. He listened, asked questions, hummed and ahed. Then he asked "were there any casualties?"

The Defense Chief nodded. "Three Brazilian soldiers were killed"

"Oh my God." said the President. He clutched the edge of his desk. A tear appeared at the edge of his eye. "My God."

The Chiefs glanced at one another, unsure how to respond to the President’s obvious grief. Finally he looked up.

"How many millions in a brazillion?"

Oh-kay… not sure where that one came from. Ahem.

So, I got my computer to make a video, showing how to construct a square with a ruler and a compass. You can see it here.

Back to big numbers. A number of years ago, I ran a Big Numbers Contest through my website. Kids had to come up with the biggest number they could write in a two inch by four inch box. You’d think that out of the infinity of numbers, there’d be a clear winner. Astoundingly, the competition ended in a draw

The rules said kids couldn’t write "Infinity". The obvious reason is that that would make the contest too easy. The real reason is that "Infinity" isn’t a well-defined number. There are actually different sizes of infinity. 

Some of the paradoxes of infinity were made clear to me by a short story by Stanislaw Lem, in this book. I read it a long time ago. You may find similar presentations by googling Hilbert’s Hotel Paradox. 

Yours,
Michael Hartley

 

 


To see the newletter archives, This Link
If you do not want to receive any more newsletters, this link
To update your preferences and to unsubscribe visit this link
Forward a Message to Someone this link

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Prickles, Lizards, Ogres, Collectible Cards and Calculus

[This is a back-issue of one of this site’s newsletters]

The other day, after a walk, I found a double-gee seed stuck in my shoe. A nasty little weed. Lucky I was wearing shoes!

It reminded me of a story of how kids used to sell these seeds to visiting sailors, claiming they were the eggs of a lizard called the Thorny Dragon. This lizard is quite amazing. One of its tricks is that water condensing on its body makes its way via capillary action to the mouth – a useful trick for a desert reptile!

Continue reading Prickles, Lizards, Ogres, Collectible Cards and Calculus