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Why is the number 1729 special?

It's the smallest number expressible as the sum of two cubes in two different ways." 1729 is the sum of the cubes of 10 and 9. Cube of 10 is 1000 and the cube of 9 is 729. Both the cubes, therefore, add up to 1729.

businesstoday.in - National Mathematics Day: Why is 1729 special - magic of Hardy ...

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Born in Tamil Nadu's Erode on December 22, 1887, the self-taught mathematical prodigy Srinivasa Ramanujan made extraordinary contributions to mathematical analysis, number theory, infinite series and continued fractions. He was fascinated by numbers and made some remarkable contributions to the partitio numerorum branch of mathematics that deals with the study of partitions of numbers. The mathematical genius compiled approximately 3900 results independently before his untimely demise in Kumbhakonam at the age of 32 due to tuberculosis.

Why 1729 is a special number?

His most popular discovery, however, remains the Hardy-Ramanujan number to this date. The Hardy-Ramanujan number stems from an anecdote wherein the British mathematician GH Hardy had gone to meet S Ramanujan in hospital. Hardy said that he came in a taxi having the number '1729', which the British mathematician described "as rather a dull one". Ramanujan replied to this saying, "No Hardy, it's a very interesting number! It's the smallest number expressible as the sum of two cubes in two different ways." 1729 is the sum of the cubes of 10 and 9. Cube of 10 is 1000 and the cube of 9 is 729. Both the cubes, therefore, add up to 1729. 1729 is also the sum of the cubes of 12 and 1. Cube of 12 is 1728 and the cube of 1 is 1. Both the cubes, therefore, add up to 1729. This certainly is a fascinating discovery and is the easiest to remember among all of Ramanujan's works. This day was first observed when the then Prime Minister Dr Manmohan Singh declared Ramanujan's birthday as National Mathematics Day on February 26,2012 upon his Madras University visit to pay tribute to Ramanujan's accomplishments and celebrated his 125th anniversary. Also read: Google Doodle celebrates Winter Solstice 2020 and the Great Conjunction; Here's what you need to know

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Why do you always get 1089?

The Math Behind the Fact: Since the digits were decreasing, (a-c) is at least 2 and no greater than 9, so the result must be one of 198, 297, 396, 495, 594, 693, 792, or 891. When you add any one of those numbers to the reverse of itself, you get 1089! See the reference for more mathematical magic tricks.

math.hmc.edu - Magic 1089 – Math Fun Facts

Here’s a cool mathematical magic trick. Write down a three-digit number whose digits are decreasing. Then reverse the digits to create a new number, and subtract this number from the original number. With the resulting number, add it to the reverse of itself. The number you will get is 1089! For example, if you start with 532 (three digits, decreasing order), then the reverse is 235. Subtract 532-235 to get 297. Now add 297 and its reverse 792, and you will get 1089!

Presentation Suggestions:

You might ask your students to see if they can explain this magic trick using a little algebra.

The Math Behind the Fact:

If we let a, b, c denote the three digits of the original number, then the three-digit number is 100a+10b+c. The reverse is 100c+10b+a. Subtract: (100a+10b+c)-(100c+10b+a) to get 99(a-c). Since the digits were decreasing, (a-c) is at least 2 and no greater than 9, so the result must be one of 198, 297, 396, 495, 594, 693, 792, or 891. When you add any one of those numbers to the reverse of itself, you get 1089!

See the reference for more mathematical magic tricks.

How to Cite this Page:

Su, Francis E., et al. “Magic 1089.” Math Fun Facts. .

References:

A. Benjamin and M. Shermer, Secrets of Mental Math, Three Rivers Press, 2006.

Fun Fact suggested by:

Francis Su

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