Archive for April, 2018

The Strange One

Monday, April 30th, 2018

¨Master, why is one not a prime number?”

“Who told you that, Lanoo?” said the Master.

“I read it in a book on number theory,” replied Lanoo.

“Actually, one is a proto prime number, from which all numbers are derived,” said the Master, “mathematicians don’t know what to do with it as it is a philosophical issue.”

“Let’s do an experiment, Lanoo,” said the Master.

“I’m ready with my notebook, calculator and pen, Master,” said Lanoo.

“Lanoo, start with the number one and add one divided by one plus one, divided by one plus one, divided by one plus one, divided by one plus one, divided by one plus one, divided by one plus one, divided by one plus one, divided by one plus one. That should do.”

“Written down, Master, ” said Lanoo.

“Add it all up and you’ll get a special number,” said the Master.

“This is quite difficult,” said Lanoo.

“Keep your tongue straight and it will all work out,” advised the Master.

After a while, Lanoo obtained the final result.

“I’ve got the number, Master,” said Lanoo.

“Very good. We call this number phi.”

Now square the number and subtract the number from its square,” said the Master.

“What do you have left?”

“Why, I have one left,” said an astounded Lanoo.

“You see why the one is so special?” said the Master, “you can do this with no other number.”

“Now, measure the length of your finger tip and multiply it by phi and you will get the length of the next phalange of your finger. If you multiply the next phalange by phi, you will get the length of the third phalange of your finger,” said the Master.

“Correct, and amazing,” said Lanoo.

“You will find that other proportions in your body also reflect phi, also called the Golden Ratio, which gives the most aesthetically pleasing Golden Rectangle,” said the Master.

“Note the following phi ratios: floor to navel/navel to top of head, tip of chin to eyes/tip of chin to tip of nose,” said the Master.

“Thus, the number one is propagated everywhere in Nature as you will see on investigating the proportions of minerals, plants and animals,” said the Master.

“The Golden Ratio represents the esoteric maxim: ‘As above, so below’ – all based on the number one,” said the Master.

“This concept was presented in the Emerald Tablet of Hermes Trismegistus:

‘That which is below corresponds to that which is Above, and that which is Above, corresponds to that which is Below, to accomplish the miracles of the One Thing.’”

“Thank you for this valuable lesson on one, Master,” said Lanoo “I will verify these indications.”

“Wishing you further illumination, Lanoo,” said the Master

 

Can you work out what the number phi is to four significant digits?

 

 

 

 

The Missing Diagonal

Saturday, April 28th, 2018

While Jill was sitting at the Chez Antoine café concentrating on a travel magazine, Jack walked in and sat down, placing his backpack in a chair.

“Hi Jill, what’s up?” said Jack full of cheer, ordering a coffee from a waitress by sign language.

“I’m looking at this curious square with numbers in it,” said Jill scratching her head, “there is a prize to be won if you can figure out what the missing numbers along the diagonal are.”

“What’s the prize,” inquired Jack with interest.

“A two-week fully paid vacation for two on the Costa del Sol of Spain,” said Jill.

“Really!! I was just thinking of going there. Let me have a look at the square,” said Jack eagerly, extending his arm.

Jill handed over the magazine with a page open that displayed the square:

190 193 164 172 191
195 163 194 186 165
184 179 181 169 183
173 178 176 188 174
192 171 177 180 162
166 185 187 170 167

“That’s a magic square,” said Jack, “I can work it out, no problem.”

“Great, then we can send in the correct answer to the magazine right away. Maybe our answer will arrive before anyone else’s,” said Jill as she handed Jack a notepad and a pen.

“Consider it done,” said Jack with a broad smile, “my Jupiter is conjunct Venus today.”

Soon, Jill paid for the coffee, and they left the Chez Antoine in a hurry.

Can you work out the missing diagonal in the magic square?

A Berber Family Bus Ride

Friday, April 27th, 2018

In Casablanca, members of the Assaidi Berber family got on a bus for a trip to Safi. The party consisted of men, women and children, twenty in all.

The bus driver said they would have to pay 20 dirhams, 3 for men, 2 for women and ½ for children.

How many men, women and children would you say went along on the trip to Safi?

 

The Yo-Yo Sale

Monday, April 23rd, 2018

Josef Fishbein, owner of the Acme Novelty Store, received a consignment of yo-yos from a supplier in India.

Josef Fishbein offered the yo-yos for sale at the price of one dollar, figuring he would make a handsome profit since there were a lot of kids living in Bearville.

But, sales were poor for quite a while and Josef Fishbein saw his profits float away like a lost balloon.

Then, one afternoon, a happy boy named Dennis came to buy a yo-yo, but did not have quite enough money to pay for it.

As the young boy reminded Josef Fishbein of his grandson Moishe who lived far away, he let Dennis have the yo-yo at a cheaper price, and decided to lower the price to this level for good luck.

Next day, the Acme Novelty Store was flooded with young boys who bought all the yo-yos. Dennis had started a fad of swinging the yo-yo in a loop in a fanciful way, so all his friends had to do it.

Josef Fishbein was very happy to sell his entire stock of yo-yos for $259.79.

Can you work out how many yo-yos Josef Fishbein sold? And the new price?