742 – 247 = 495

Reverse this result and add, so:

495 + 594 = 1089

This answer, 1089, will result from any 3 digit number where the first and last digits differ by at least 2.

Take any 3 digit number, abc. Writing the subtraction (this time taking the reversed number from the original – it doesn’t matter which way round it goes) gives:

abc – cba = 100a -100c – a – c    (the b’s in the tens column cancel out)

= 99a – 99c  =  99(a-c)

Since a and c differ by at least 2, the possible values of a-c are: 2,3,4,5,6,7,8

So, 99(a-c) must equal one of the following: 198, 297, 396, 495, 594, 693, 792

Now say that the result of abc – cba  is xyz

Then the end result, e,  of adding xyz to zyx  can be written as 100x + 10y + z + 100z + 10y + x

e = 100(x+z) + 20y +x + z

But from our list of possible values of 99(a-c), we can can see that the middle digit, y, is always 9. Also, the addition of the two end digits is always 9. So x+z = 9.

So our final sum e = 100(9) + 20(9) + 9

e= 900 + 180 + 9

e=1089

Always.

QED!

Phew! And that’s a simple proof by any mathematical standard.

(Pi by Mykl Roventine)

The 14th March (3/14 in American date notation) has over recent years become Pi day because it famously starts with 3.14

New Scientist magazine posted several fascinating facts about Pi and it seemed apropos to share them with you. Did you know..

• you can use the stars to calculate Pi
• ….or the rivers on Earth
• Pi has inspired a literary genre where the number of letters in words successively follow the Pi digits
• you can calculate Pi with some needles and lined paper
• every book ever written is coded within the digits of Pi

For explanation of all these see the NS website and enjoy a nice slice of Pi.

The ancient Egyptian mummy of famous King Rameses the Great, or Rameses II as he is more commonly known had his own real-life passport! On the passport it listed his occupation as “King (deceased)”!

In 1974, the mummy had to be flown from the Cairo Museum to Paris where experts could examine it’s rapidly deteriorating condition. Scientific analysis in Paris revealed a fungal infection, for which the ancient cadaver was treated. The examination also revealed old battle wounds and bone fractures in addition to the Pharaoh’s poor circulation and arthritis.

The king was an incredible 90 years old when he died, after a rule of 67 years – at a time when the life expectancy was only a few decades. He was also taller than average, about 6 feet tall in comparison to the average Egyptian at just over 5 feet.

By the time of his death, Ramesses was suffering from severe dental problems and was plagued by arthritis and hardening of the arteries. When he finally died, he was about 90 years old. He had outlived many of his wives and children and left great memorials all over Egypt, especially to his beloved first queen Nefertari. Nine more pharaohs would take the name Ramesses in his honour, but few ever equalled his greatness. Nearly all of his subjects had been born during his reign and thought the world might end without him.

Ramesses II did become the legendary figure he so desperately wanted to be, but this was not enough to protect Egypt. New enemies were attacking the empire which also suffered internal problems and it could not last. Less than 150 years after Ramesses died, the Egyptian empire fell, his descendants lost their power and the New Kingdom came to an end.

wikipedia

The great Romantic poet died aged just 37 from a complication of dental surgery resulting in blood poisoning and aggravation of his long-standing rheumatic heart condition. The image of the alcoholic philanderer was wide of the mark. Like many a man of the time, and since, Rob enjoyed life’s pleasures, but was no brute. The Edinburgh literati worked to sentimentalise Burns during his life and after his death, dismissing his education by calling him a “heaven-taught ploughman”. The truth is that Burns, while not of aristocratic birth, was certainly schooled and had a firm grasp of literature and classics.

Despite his tragically short life, Burns has had arguably more worldwide influence than any other poet. His themes of freedom, fraternity and love, being masterfully presented, have won him admirers in every country. When asked to say which lyric or verse was the greatest influence on his own work, Bob Dylan chose “My Luve is Like a Red, Red Rose,” by Burns.

Burns night is the celebration of his life and work, marked each 25th of January on the poet’s birthday. Burns suppers are held round the world, with readings and songs and of course the famous haggis, tatties and neeps.

In 2009, in a poll by Scottish Television, Robert Burns was voted by his own countrymen as the Greatest Ever Scot, narrowly beating William Wallace  into second place.

More iformation on wikipedia