Comments on: Three Tricks for Squaring Numbers http://www.logicnest.com/archives/9 The personal weblog of Ian Luke Kane. Thoughts on mathematics, logic, and life. The beauty therein and the strangeness of it all. Sat, 30 Aug 2008 00:04:14 +0000 http://wordpress.org/?v=2.5.1 By: Matt http://www.logicnest.com/archives/9#comment-6430 Matt Tue, 01 Apr 2008 02:48:28 +0000 http://www.ianluke.exteroceptions.com/?p=9#comment-6430 Just curious if anyone still reads this, i came up with something, but i don't want to post if no one is going to read it Just curious if anyone still reads this, i came up with something, but i don’t want to post if no one is going to read it

]]> By: Case http://www.logicnest.com/archives/9#comment-6411 Case Wed, 09 Jan 2008 17:41:45 +0000 http://www.ianluke.exteroceptions.com/?p=9#comment-6411 I too came up with the (a|n)^2 = a0^2 + n(a|n+a0) as described earlier while on my way to work and I must say that for the hard ones this seems to be the quickest mental way for me to do it... that is to say I can typically solve in 30 seconds or less with it now. I too came up with the (a|n)^2 = a0^2 + n(a|n+a0) as described earlier while on my way to work and I must say that for the hard ones this seems to be the quickest mental way for me to do it… that is to say I can typically solve in 30 seconds or less with it now.

]]> By: Ian Luke Kane http://www.logicnest.com/archives/9#comment-95 Ian Luke Kane Tue, 21 Mar 2006 12:58:03 +0000 http://www.ianluke.exteroceptions.com/?p=9#comment-95 Jenna, unfortunately I do believe that all of these methods have been discovered long ago, although I'm sure it's the case in mathematics that some very simple conjectures have gone a long time without having been stated. Take the Beal Conjecture, for instance. With all the talk of Fermat's Last Theorem no one had stated the more generalized conjecture until literally hundreds of years later. Jenna, unfortunately I do believe that all of these methods have been discovered long ago, although I’m sure it’s the case in mathematics that some very simple conjectures have gone a long time without having been stated. Take the Beal Conjecture, for instance. With all the talk of Fermat’s Last Theorem no one had stated the more generalized conjecture until literally hundreds of years later.

]]> By: Jenna http://www.logicnest.com/archives/9#comment-93 Jenna Tue, 21 Mar 2006 09:32:39 +0000 http://www.ianluke.exteroceptions.com/?p=9#comment-93 hey; the first method you have here I've wondered, is this a published theorum? I came up with it once myself and showed my precal teacher, who said that yes, she did recognize it. Also, though.. it can be extrapolated further if you have the spare time. (a+n)^2= a^2 + n[a + [a+n)] 22^2 = 484 20^2 + 2(20+22) = 484 For any positive nonzero number a, the square of a+n will equal the square of a plus n[a + (a+n)]. hey; the first method you have here I’ve wondered, is this a published theorum? I came up with it once myself and showed my precal teacher, who said that yes, she did recognize it. Also, though.. it can be extrapolated further if you have the spare time.

(a+n)^2= a^2 + n[a + [a+n)]

22^2 = 484

20^2 + 2(20+22) = 484

For any positive nonzero number a, the square of a+n will equal the square of a plus n[a + (a+n)].

]]> By: Aung Khaing http://www.logicnest.com/archives/9#comment-43 Aung Khaing Sun, 05 Mar 2006 23:06:09 +0000 http://www.ianluke.exteroceptions.com/?p=9#comment-43 Hi Ian and Nand, My name is Aung Khaing, a sophomore student in the University of Arkansas, Fayetteville. I also like to play with numbers like you do. I devised a general formula for any squares. Please see how you like that. Because of the limited way to experess my thought on this web, all I can do is to type into Excel and copy it. If you would have a chance to see it in Microsoft word explanation and Microsoft equation editor, you would see more clearly. If you do that on paper you don't really need to wirte down all the zeros. You can just leave blanks in places of zeros (eg. four blanks for 10^4)and can fill in with nonzero numbers. In this way, you only need 3 lines on paper to square 3 digit number and add them up. For any 2 digit number, you can square it in mind. For now, this is the best way I can transfer my thought. You can just copy the following formula into and excel and test it. For 2 digit numbers, treat them like AB^2. =(((10^2)*(A1^2))+(B1^2)+(2*(10)*(A1*B1))) For 3 digits numbers, treat them like ABC^2. =(((10^4)*(A1^2))+((10^2)*(B1^2))+(C1^2) +(2*(10^3)*(A1*B1))+(2*(10^2)*(A1*C1))+(2*(10)*(B1*C1))) For 4 digits numbers, treat it like ABCD^2. =(((10^6)*(A1^2))+((10^4)*(B1^2))+((10^2)*(C1^2))+(D1^2) +(2*(10^5)*(A1*B1))+(2*(10^4)*(A1*C1))+(2*(10^3)*(A1*D1)) +(2*(10^3)*(B1*C1))+(2*(10^2)*(B1*D1))+(2*(10)*(C1*D1))) For 5 digits numbers, treat it like ABCDE^2. =(((10^8)*(A1^2))+((10^6)*(B1^2))+((10^4)*(C1^2)) +((10^2)*(D1^2))+(E1^2)+(2*(10^7)*(A1*B1))+(2*(10^6)*(A1*C1)) +(2*(10^5)*(A1*D1))+(2*(10^4)*(A1*E1))+(2*(10^5)*(B1*C1)) +(2*(10^4)*(B1*D1))+(2*(10^3)*(B1*E1))+(2*(10^3)*(C1*D1)) +(2*(10^2)*(C1*E1))+(2*(10)*(D1*E1))) Sincerely, Aung Khaing :) Sophomore, University of Arkansas, Fayetteville Hi Ian and Nand,

My name is Aung Khaing, a sophomore student in the University of Arkansas, Fayetteville. I also like to play with numbers like you do. I devised a general formula for any squares. Please see how you like that. Because of the limited way to experess my thought on this web, all I can do is to type into Excel and copy it.

If you would have a chance to see it in Microsoft word explanation and Microsoft equation editor, you would see more clearly. If you do that on paper you don’t really need to wirte down all the zeros. You can just leave blanks in places of zeros (eg. four blanks for 10^4)and can fill in with nonzero numbers. In this way, you only need 3 lines on paper to square 3 digit number and add them up. For any 2 digit number, you can square it in mind.

For now, this is the best way I can transfer my thought. You can just copy the following formula into and excel and test it.

For 2 digit numbers, treat them like AB^2.
=(((10^2)*(A1^2))+(B1^2)+(2*(10)*(A1*B1)))

For 3 digits numbers, treat them like ABC^2.
=(((10^4)*(A1^2))+((10^2)*(B1^2))+(C1^2)

+(2*(10^3)*(A1*B1))+(2*(10^2)*(A1*C1))+(2*(10)*(B1*C1)))

For 4 digits numbers, treat it like ABCD^2.
=(((10^6)*(A1^2))+((10^4)*(B1^2))+((10^2)*(C1^2))+(D1^2)

+(2*(10^5)*(A1*B1))+(2*(10^4)*(A1*C1))+(2*(10^3)*(A1*D1))

+(2*(10^3)*(B1*C1))+(2*(10^2)*(B1*D1))+(2*(10)*(C1*D1)))

For 5 digits numbers, treat it like ABCDE^2.
=(((10^8)*(A1^2))+((10^6)*(B1^2))+((10^4)*(C1^2))

+((10^2)*(D1^2))+(E1^2)+(2*(10^7)*(A1*B1))+(2*(10^6)*(A1*C1))

+(2*(10^5)*(A1*D1))+(2*(10^4)*(A1*E1))+(2*(10^5)*(B1*C1))

+(2*(10^4)*(B1*D1))+(2*(10^3)*(B1*E1))+(2*(10^3)*(C1*D1))

+(2*(10^2)*(C1*E1))+(2*(10)*(D1*E1)))

Sincerely,
Aung Khaing :)
Sophomore, University of Arkansas, Fayetteville

]]> By: N. L. Shraman http://www.logicnest.com/archives/9#comment-21 N. L. Shraman Sat, 31 Dec 2005 11:00:53 +0000 http://www.ianluke.exteroceptions.com/?p=9#comment-21 Dear Ian, My full name is Nand Lal Shraman. I am from Kanpur, India. I have already responded your methods of squaring. Today I am going to describe the method for squaring large numbers say three digits in a very easy way. For example : What is the square of 425 ? here is the method: Step 1 Multiply 5*5 (Unit*Unit)=25 carry 2 leave 5 Step 2 Multiply 5*2(unit*tense)*2=20 ,add 2=22 carry 2,leave2 Step 3 Multiply 5*4*2+2*2= 44 add 2=46 carry 4 leave 6 ( Unit*hundredth)*2 + TENSE*2 Step 4 Multiply 2*4*2 add 4=20 ,carry 2 leave 0 (tense*hundredth)*2 add carry Step 5 Multiply 4*4 add 2=18 leave 18 (Multiply hundredth*hundredth add 4 The answer is 180625 However it looks somewhat difficult but it as easy as 1,2,3... Let me describe again: Multiply U*U Multiply U*T double it and add carry leave unit Multiply U*H double it + T*T add carry, leave unit Multiply T*H double it add carry leave unit Multiply H*H add carry leave it. Next Time I will decribe how to mutiply or square large numbers of 4,5,6,7,8,9,10,11,12 digits etc. It is a fun once you start calculating. Yours Own N. L. Shraman Top trainer of math and memory in India Dear Ian,
My full name is Nand Lal Shraman. I am from Kanpur, India. I have already responded your methods of squaring. Today I am going to describe the method for squaring large numbers say three digits in a very easy way. For example :
What is the square of 425 ? here is the method:
Step 1 Multiply 5*5 (Unit*Unit)=25 carry 2 leave 5
Step 2 Multiply 5*2(unit*tense)*2=20 ,add 2=22 carry 2,leave2
Step 3 Multiply 5*4*2+2*2= 44 add 2=46 carry 4 leave 6
( Unit*hundredth)*2 + TENSE*2
Step 4 Multiply 2*4*2 add 4=20 ,carry 2 leave 0
(tense*hundredth)*2 add carry
Step 5 Multiply 4*4 add 2=18 leave 18
(Multiply hundredth*hundredth add 4
The answer is 180625
However it looks somewhat difficult but it as easy as 1,2,3… Let me describe again:
Multiply U*U
Multiply U*T double it and add carry leave unit
Multiply U*H double it + T*T add carry, leave unit
Multiply T*H double it add carry leave unit
Multiply H*H add carry leave it.
Next Time I will decribe how to mutiply or square large numbers of 4,5,6,7,8,9,10,11,12 digits etc.
It is a fun once you start calculating.
Yours Own
N. L. Shraman
Top trainer of math and memory in India

]]> By: N L Shraman http://www.logicnest.com/archives/9#comment-18 N L Shraman Fri, 04 Nov 2005 15:15:20 +0000 http://www.ianluke.exteroceptions.com/?p=9#comment-18 MULTIPLY THE NUMBERS WHOSE SUM OF UNITS IS 10 AND TENS ARE SAME Just multiply unit by unit and tens by ( tens+1) e.g. 83x87= 8x(8+1)=72 and 3x7=21 The Ans is 72 21 MULTIPLY THE NUMBERS WHOSE SUM OF UNITS IS 10 AND TENS ARE SAME
Just multiply unit by unit and tens by ( tens+1) e.g.

83×87= 8x(8+1)=72 and 3×7=21

The Ans is 72 21

]]> By: N L Shraman http://www.logicnest.com/archives/9#comment-17 N L Shraman Fri, 04 Nov 2005 15:09:47 +0000 http://www.ianluke.exteroceptions.com/?p=9#comment-17 excuse me for some words are not spelled correctly due to poor response n site. excuse me for some words are not spelled correctly due to poor response n site.

]]> By: N L Shraman http://www.logicnest.com/archives/9#comment-16 N L Shraman Fri, 04 Nov 2005 15:08:13 +0000 http://www.ianluke.exteroceptions.com/?p=9#comment-16 Dear Ian, I am a mental math and mental memory trainer of India, you may discuss any problem related to the math and memory. You may visit my site for detail http://unlimitedmemory.tripod.com Dear Ian, I am a mental math and mental memory trainer of India, you may discuss any problem related to the math and memory. You may visit my site for detail http://unlimitedmemory.tripod.com

]]> By: Ian Luke Kane http://www.logicnest.com/archives/9#comment-15 Ian Luke Kane Fri, 04 Nov 2005 14:54:46 +0000 http://www.ianluke.exteroceptions.com/?p=9#comment-15 Thanks N L Shraman, I appreciate it! I'll have to keep that in mind for the future... Thanks N L Shraman, I appreciate it! I’ll have to keep that in mind for the future…

]]> By: N L Shraman http://www.logicnest.com/archives/9#comment-14 N L Shraman Fri, 04 Nov 2005 14:46:14 +0000 http://www.ianluke.exteroceptions.com/?p=9#comment-14 There is another very easy metod to make a sqare: Suppose you have to find out 43^2, just start writing from the right side (i) 3*3=9 (unit multiplied by unit) (ii) (3*4)*2=12 write 2 carry one (unit*tens and double it) (iii) 4*4=16 add carry 1, write 17 (tens*tens) The answer is 17 2 9 There is another very easy metod to make a sqare:

Suppose you have to find out 43^2, just start writing from the right side
(i) 3*3=9 (unit multiplied by unit)
(ii) (3*4)*2=12 write 2 carry one (unit*tens and double it)
(iii) 4*4=16 add carry 1, write 17 (tens*tens)
The answer is 17 2 9

]]> By: Adam Anderson http://www.logicnest.com/archives/9#comment-2 Adam Anderson Wed, 31 Aug 2005 15:43:17 +0000 http://www.ianluke.exteroceptions.com/?p=9#comment-2 hey ian - thanks for the lesson. i wanted to say hey and let you know i think of you often. it's funny when i talk to scott; he reminds me a lot of you, and it's been good to have the opportunity to talk to him as much as i have. in any case, i want to hear how life is for you and what's new and old and obscure and pointless as well. i'm in erie currently (and will be for three years hence), so if you feel like a 2 hour trip for a coffee, beer, and conversation, feel free to come up. also, give emily my good wishes. peace, adam hey ian -

thanks for the lesson.

i wanted to say hey and let you know i think of you often. it’s funny when i talk to scott; he reminds me a lot of you, and it’s been good to have the opportunity to talk to him as much as i have.

in any case, i want to hear how life is for you and what’s new and old and obscure and pointless as well. i’m in erie currently (and will be for three years hence), so if you feel like a 2 hour trip for a coffee, beer, and conversation, feel free to come up.

also, give emily my good wishes.

peace,
adam

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