## Monday, March 16, 2015

### 10 Math/Number Facts (Vol. #2)

1. Another mnemonic for remembering the first 20 decimals of pi is

*How I wish I could enumerate pi easily, since all these bullshit mnemonics prevent recalling any of pi's sequence more simply. (posted by abyssbrain in comment of previous post)*

*2. 6666 days is equal to 144 hours + 1440 hours + 14400 hours + 144000 hours.*

3. One cycle of the Mayan calendar is equivalent to 5126 years. The digits 5126 begin at the 2012th decimal place of π!

4. Metric Day is celebrated each year on October 10th.

5. 68 is the smallest composite number that can be read as a prime number when it is turned upside down.

6. 71 is the largest prime p that humans will ever discover such that 2^p doesn't contain the digit 9.

7. Welsh government has declared March 14 as Pi Day Cymru as a way of honouring the Anglesey-born mathematician William Jones, who came up with the idea of pi in 1706.

8. Mats Bergsten of Sweden holds the world record for memorising pi while juggling, reciting 9,778 digits in 1hr 20min.

9. A poem written such that the length of each word is determined by the digits in pi is called a piem. A haiku written under those constraints is called a piku.

10. Among all shapes with the same perimeter, the circle has the largest area.

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William Jones

## Monday, March 9, 2015

### 10 Quotes on Math

1. "A mathematician is a device for turning coffee into theorems." - Alfréd Rényi

2. "Proof is the idol before whom the pure mathematician tortures himself." - Sir Arthur Eddington

3. "Mathematics is about progress and adventure and emotion" - Cédric Villani

4. "Math is not about memorizing formulas. Math is about understanding the world." - Anonymous

5. "Mathematics is capable of an artistic excellence as great as that of any music, perhaps greater." - Bertrand Russell

6. "The essence of mathematics lies precisely in its freedom." - Georg Cantor

7. "Don't just read it; fight it! Ask your own questions, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? What happens in the classical special case? What about the degenerate cases? Where does the proof use the hypothesis?" - Paul Halmos

8. "Wherever there is number, there is beauty." - Diadochus Proclus

9. "Statistics: The only science that enables different experts using the same figures to draw different conclusions." - Evan Esar

10. "But mathematics is the sister, as well as the servant, of the arts and is touched by the same madness and genius." - Marston Morse

5. "Mathematics is capable of an artistic excellence as great as that of any music, perhaps greater." - Bertrand Russell

6. "The essence of mathematics lies precisely in its freedom." - Georg Cantor

7. "Don't just read it; fight it! Ask your own questions, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? What happens in the classical special case? What about the degenerate cases? Where does the proof use the hypothesis?" - Paul Halmos

8. "Wherever there is number, there is beauty." - Diadochus Proclus

9. "Statistics: The only science that enables different experts using the same figures to draw different conclusions." - Evan Esar

10. "But mathematics is the sister, as well as the servant, of the arts and is touched by the same madness and genius." - Marston Morse

## Saturday, March 7, 2015

### Top 10 Pi jokes for Pi day

- What do you get when you cut a jack o’lantern by its diameter?… Pumpkin Pi!
- What do you get when you take green cheese and divide its circumference by its diameter?… Moon Pi.
- What do you get when you take the sun and divide its circumference by its diameter?…Pi in the sky.
- Mathematician: “Pi r squared” Baker:” No! Pies are round, cakes are square!
- What do we get when we take the object and order the rim by the diameter?…Pi in the sky by and by.
- In Alaska, where it gets very cold, pi is only 3.00. As you know, everything shrinks in the cold. They call it Eskimo pi.
- What do you get if you divide the circumference of a bowl of ice cream by its diameter?… Pi a’la mode.
- 3.14% of Sailors are PI rates.
- The roundest knight at King Arthur’s was Sir Cumference… He ate too much Pi!
- What is the official animal of Pi Day?… the PI – thon!

Labels:
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## Wednesday, March 4, 2015

### 10 Math/Number Facts

1. The word ‘hundrath’ in Old Norse, from which our ‘hundred’ derives, meant not 100 but 120.

2. 3435 - A Münchhausen Number has the property that the sum of its digits raised to themselves produces the original number. The only Münchhausen Number are 1 and 3435 (3435 = 3^3 + 4^4 + 3^3 + 5^5)

3. 2520 is the smallest number divisible by the numbers 1 through 10.

4. You can remember the value of Pi (3.1415926) by counting each word's letters in 'May I have a large container of coffee'.

5. If A=1,... Z=26, then the word PRIME is prime. (P+R+I+M+E --> 16+18+9+13+5 =61)

6. No Fibonacci number is divisible by 61.

7. 61!-60!+59!-...+1! is prime.

8. In base two number system, pi is 11.001001000011...

9. The digits 62 occur at the 61st & 62nd digits of phi, φ; AND The 61st & 62nd digits of e.

10. The 61st Fibonacci number (2,504,730,781,961) is the smallest Fibonacci number which contains all the digits from 0 to 9.

2. 3435 - A Münchhausen Number has the property that the sum of its digits raised to themselves produces the original number. The only Münchhausen Number are 1 and 3435 (3435 = 3^3 + 4^4 + 3^3 + 5^5)

3. 2520 is the smallest number divisible by the numbers 1 through 10.

4. You can remember the value of Pi (3.1415926) by counting each word's letters in 'May I have a large container of coffee'.

5. If A=1,... Z=26, then the word PRIME is prime. (P+R+I+M+E --> 16+18+9+13+5 =61)

6. No Fibonacci number is divisible by 61.

7. 61!-60!+59!-...+1! is prime.

8. In base two number system, pi is 11.001001000011...

9. The digits 62 occur at the 61st & 62nd digits of phi, φ; AND The 61st & 62nd digits of e.

10. The 61st Fibonacci number (2,504,730,781,961) is the smallest Fibonacci number which contains all the digits from 0 to 9.

## Sunday, March 1, 2015

### Interesting factorizations| Num3ers 7928 and 7929

Recently

Benjamin Vitale posted interesting relationship between numbers 7928 and 7928 on his blog in his article article here

The two consecutive numbers can be expressed as follows

7928 = 8 * 991

7929 = 9 * 881

So, I wrote little python script to find more pairs like this and posting it as below.

And It is interesting to find that all 3-digit multipliers are ending with 1.201 * 3 = 603 and 301 * 2 = 602

221 * 1 = 221 and 111 * 2 = 222

221 * 3 = 663 and 331 * 2 = 662

301 * 2 = 602 and 201 * 3 = 603

301 * 4 = 1204 and 401 * 3 = 1203

331 * 2 = 662 and 221 * 3 = 663

331 * 4 = 1324 and 441 * 3 = 1323

401 * 3 = 1203 and 301 * 4 = 1204

401 * 5 = 2005 and 501 * 4 = 2004

441 * 3 = 1323 and 331 * 4 = 1324

441 * 5 = 2205 and 551 * 4 = 2204

501 * 4 = 2004 and 401 * 5 = 2005

501 * 6 = 3006 and 601 * 5 = 3005

551 * 4 = 2204 and 441 * 5 = 2205

551 * 6 = 3306 and 661 * 5 = 3305

601 * 5 = 3005 and 501 * 6 = 3006

601 * 7 = 4207 and 701 * 6 = 4206

661 * 5 = 3305 and 551 * 6 = 3306

661 * 7 = 4627 and 771 * 6 = 4626

701 * 6 = 4206 and 601 * 7 = 4207

701 * 8 = 5608 and 801 * 7 = 5607

771 * 6 = 4626 and 661 * 7 = 4627

771 * 8 = 6168 and 881 * 7 = 6167

801 * 7 = 5607 and 701 * 8 = 5608

801 * 9 = 7209 and 901 * 8 = 7208

881 * 7 = 6167 and 771 * 8 = 6168

881 * 9 = 7929 and 991 * 8 = 7928

901 * 8 = 7208 and 801 * 9 = 7209

991 * 8 = 7928 and 881 * 9 = 7929

**UPDATE**

**all 4-digits numbers (Those too ending with 1)**

2001 * 1 = 2001 and 1001 * 2 = 2002

2001 * 3 = 6003 and 3001 * 2 = 6002

2021 * 1 = 2021 and 1011 * 2 = 2022

2021 * 3 = 6063 and 3031 * 2 = 6062

2201 * 1 = 2201 and 1101 * 2 = 2202

2201 * 3 = 6603 and 3301 * 2 = 6602

2221 * 1 = 2221 and 1111 * 2 = 2222

2221 * 3 = 6663 and 3331 * 2 = 6662

3001 * 2 = 6002 and 2001 * 3 = 6003

3001 * 4 = 12004 and 4001 * 3 = 12003

3031 * 2 = 6062 and 2021 * 3 = 6063

3031 * 4 = 12124 and 4041 * 3 = 12123

3301 * 2 = 6602 and 2201 * 3 = 6603

3301 * 4 = 13204 and 4401 * 3 = 13203

3331 * 2 = 6662 and 2221 * 3 = 6663

3331 * 4 = 13324 and 4441 * 3 = 13323

4001 * 3 = 12003 and 3001 * 4 = 12004

4001 * 5 = 20005 and 5001 * 4 = 20004

4041 * 3 = 12123 and 3031 * 4 = 12124

4041 * 5 = 20205 and 5051 * 4 = 20204

4401 * 3 = 13203 and 3301 * 4 = 13204

4401 * 5 = 22005 and 5501 * 4 = 22004

4441 * 3 = 13323 and 3331 * 4 = 13324

4441 * 5 = 22205 and 5551 * 4 = 22204

5001 * 4 = 20004 and 4001 * 5 = 20005

5001 * 6 = 30006 and 6001 * 5 = 30005

5051 * 4 = 20204 and 4041 * 5 = 20205

5051 * 6 = 30306 and 6061 * 5 = 30305

5501 * 4 = 22004 and 4401 * 5 = 22005

5501 * 6 = 33006 and 6601 * 5 = 33005

5551 * 4 = 22204 and 4441 * 5 = 22205

5551 * 6 = 33306 and 6661 * 5 = 33305

6001 * 5 = 30005 and 5001 * 6 = 30006

6001 * 7 = 42007 and 7001 * 6 = 42006

6061 * 5 = 30305 and 5051 * 6 = 30306

6061 * 7 = 42427 and 7071 * 6 = 42426

6601 * 5 = 33005 and 5501 * 6 = 33006

6601 * 7 = 46207 and 7701 * 6 = 46206

6661 * 5 = 33305 and 5551 * 6 = 33306

6661 * 7 = 46627 and 7771 * 6 = 46626

7001 * 6 = 42006 and 6001 * 7 = 42007

7001 * 8 = 56008 and 8001 * 7 = 56007

7071 * 6 = 42426 and 6061 * 7 = 42427

7071 * 8 = 56568 and 8081 * 7 = 56567

7701 * 6 = 46206 and 6601 * 7 = 46207

7701 * 8 = 61608 and 8801 * 7 = 61607

7771 * 6 = 46626 and 6661 * 7 = 46627

7771 * 8 = 62168 and 8881 * 7 = 62167

8001 * 7 = 56007 and 7001 * 8 = 56008

8001 * 9 = 72009 and 9001 * 8 = 72008

8081 * 7 = 56567 and 7071 * 8 = 56568

8081 * 9 = 72729 and 9091 * 8 = 72728

8801 * 7 = 61607 and 7701 * 8 = 61608

8801 * 9 = 79209 and 9901 * 8 = 79208

8881 * 7 = 62167 and 7771 * 8 = 62168

8881 * 9 = 79929 and 9991 * 8 = 79928

9001 * 8 = 72008 and 8001 * 9 = 72009

9091 * 8 = 72728 and 8081 * 9 = 72729

9901 * 8 = 79208 and 8801 * 9 = 79209

9991 * 8 = 79928 and 8881 * 9 = 79929

5 digits numbers (and again ending with 1)

20001 * 1 = 20001 and 10001 * 2 = 20002

20001 * 3 = 60003 and 30001 * 2 = 60002

20021 * 1 = 20021 and 10011 * 2 = 20022

20021 * 3 = 60063 and 30031 * 2 = 60062

20201 * 1 = 20201 and 10101 * 2 = 20202

20201 * 3 = 60603 and 30301 * 2 = 60602

20221 * 1 = 20221 and 10111 * 2 = 20222

20221 * 3 = 60663 and 30331 * 2 = 60662

22001 * 1 = 22001 and 11001 * 2 = 22002

22001 * 3 = 66003 and 33001 * 2 = 66002

22021 * 1 = 22021 and 11011 * 2 = 22022

22021 * 3 = 66063 and 33031 * 2 = 66062

22201 * 1 = 22201 and 11101 * 2 = 22202

22201 * 3 = 66603 and 33301 * 2 = 66602

22221 * 1 = 22221 and 11111 * 2 = 22222

22221 * 3 = 66663 and 33331 * 2 = 66662

30001 * 2 = 60002 and 20001 * 3 = 60003

30001 * 4 = 120004 and 40001 * 3 = 120003

30031 * 2 = 60062 and 20021 * 3 = 60063

30031 * 4 = 120124 and 40041 * 3 = 120123

30301 * 2 = 60602 and 20201 * 3 = 60603

30301 * 4 = 121204 and 40401 * 3 = 121203

30331 * 2 = 60662 and 20221 * 3 = 60663

30331 * 4 = 121324 and 40441 * 3 = 121323

33001 * 2 = 66002 and 22001 * 3 = 66003

33001 * 4 = 132004 and 44001 * 3 = 132003

33031 * 2 = 66062 and 22021 * 3 = 66063

33031 * 4 = 132124 and 44041 * 3 = 132123

33301 * 2 = 66602 and 22201 * 3 = 66603

33301 * 4 = 133204 and 44401 * 3 = 133203

33331 * 2 = 66662 and 22221 * 3 = 66663

33331 * 4 = 133324 and 44441 * 3 = 133323

40001 * 3 = 120003 and 30001 * 4 = 120004

40001 * 5 = 200005 and 50001 * 4 = 200004

40041 * 3 = 120123 and 30031 * 4 = 120124

40041 * 5 = 200205 and 50051 * 4 = 200204

40401 * 3 = 121203 and 30301 * 4 = 121204

40401 * 5 = 202005 and 50501 * 4 = 202004

40441 * 3 = 121323 and 30331 * 4 = 121324

40441 * 5 = 202205 and 50551 * 4 = 202204

44001 * 3 = 132003 and 33001 * 4 = 132004

44001 * 5 = 220005 and 55001 * 4 = 220004

44041 * 3 = 132123 and 33031 * 4 = 132124

44041 * 5 = 220205 and 55051 * 4 = 220204

44401 * 3 = 133203 and 33301 * 4 = 133204

44401 * 5 = 222005 and 55501 * 4 = 222004

44441 * 3 = 133323 and 33331 * 4 = 133324

44441 * 5 = 222205 and 55551 * 4 = 222204

50001 * 4 = 200004 and 40001 * 5 = 200005

50001 * 6 = 300006 and 60001 * 5 = 300005

50051 * 4 = 200204 and 40041 * 5 = 200205

50051 * 6 = 300306 and 60061 * 5 = 300305

50501 * 4 = 202004 and 40401 * 5 = 202005

50501 * 6 = 303006 and 60601 * 5 = 303005

50551 * 4 = 202204 and 40441 * 5 = 202205

50551 * 6 = 303306 and 60661 * 5 = 303305

55001 * 4 = 220004 and 44001 * 5 = 220005

55001 * 6 = 330006 and 66001 * 5 = 330005

55051 * 4 = 220204 and 44041 * 5 = 220205

55051 * 6 = 330306 and 66061 * 5 = 330305

55501 * 4 = 222004 and 44401 * 5 = 222005

55501 * 6 = 333006 and 66601 * 5 = 333005

55551 * 4 = 222204 and 44441 * 5 = 222205

55551 * 6 = 333306 and 66661 * 5 = 333305

60001 * 5 = 300005 and 50001 * 6 = 300006

60001 * 7 = 420007 and 70001 * 6 = 420006

60061 * 5 = 300305 and 50051 * 6 = 300306

60061 * 7 = 420427 and 70071 * 6 = 420426

60601 * 5 = 303005 and 50501 * 6 = 303006

60601 * 7 = 424207 and 70701 * 6 = 424206

60661 * 5 = 303305 and 50551 * 6 = 303306

60661 * 7 = 424627 and 70771 * 6 = 424626

66001 * 5 = 330005 and 55001 * 6 = 330006

66001 * 7 = 462007 and 77001 * 6 = 462006

66061 * 5 = 330305 and 55051 * 6 = 330306

66061 * 7 = 462427 and 77071 * 6 = 462426

66601 * 5 = 333005 and 55501 * 6 = 333006

66601 * 7 = 466207 and 77701 * 6 = 466206

66661 * 5 = 333305 and 55551 * 6 = 333306

66661 * 7 = 466627 and 77771 * 6 = 466626

70001 * 6 = 420006 and 60001 * 7 = 420007

70001 * 8 = 560008 and 80001 * 7 = 560007

70071 * 6 = 420426 and 60061 * 7 = 420427

70071 * 8 = 560568 and 80081 * 7 = 560567

70701 * 6 = 424206 and 60601 * 7 = 424207

70701 * 8 = 565608 and 80801 * 7 = 565607

70771 * 6 = 424626 and 60661 * 7 = 424627

70771 * 8 = 566168 and 80881 * 7 = 566167

77001 * 6 = 462006 and 66001 * 7 = 462007

77001 * 8 = 616008 and 88001 * 7 = 616007

77071 * 6 = 462426 and 66061 * 7 = 462427

77071 * 8 = 616568 and 88081 * 7 = 616567

77701 * 6 = 466206 and 66601 * 7 = 466207

77701 * 8 = 621608 and 88801 * 7 = 621607

77771 * 6 = 466626 and 66661 * 7 = 466627

77771 * 8 = 622168 and 88881 * 7 = 622167

80001 * 7 = 560007 and 70001 * 8 = 560008

80001 * 9 = 720009 and 90001 * 8 = 720008

80081 * 7 = 560567 and 70071 * 8 = 560568

80081 * 9 = 720729 and 90091 * 8 = 720728

80801 * 7 = 565607 and 70701 * 8 = 565608

80801 * 9 = 727209 and 90901 * 8 = 727208

80881 * 7 = 566167 and 70771 * 8 = 566168

80881 * 9 = 727929 and 90991 * 8 = 727928

88001 * 7 = 616007 and 77001 * 8 = 616008

88001 * 9 = 792009 and 99001 * 8 = 792008

88081 * 7 = 616567 and 77071 * 8 = 616568

88081 * 9 = 792729 and 99091 * 8 = 792728

88801 * 7 = 621607 and 77701 * 8 = 621608

88801 * 9 = 799209 and 99901 * 8 = 799208

88881 * 7 = 622167 and 77771 * 8 = 622168

88881 * 9 = 799929 and 99991 * 8 = 799928

90001 * 8 = 720008 and 80001 * 9 = 720009

90091 * 8 = 720728 and 80081 * 9 = 720729

90901 * 8 = 727208 and 80801 * 9 = 727209

90991 * 8 = 727928 and 80881 * 9 = 727929

99001 * 8 = 792008 and 88001 * 9 = 792009

99091 * 8 = 792728 and 88081 * 9 = 792729

99901 * 8 = 799208 and 88801 * 9 = 799209

99991 * 8 = 799928 and 88881 * 9 = 799929

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