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We Can Do Many Things Without A Calculator In Mathematics.



Find The Square Of A Two-digit Number
Note:The square of a two-digit number has to be a three-digit or four-digit number.

1. The squares from 10 to 25 have to be memerized as the basic knowladge.
The chart as follow:
102=100 112=121 122=144 132=169
142=196 152=225 162=256 172=289
182=324 192=361 202=400 212=441
222=484 232=529 242=576 252=625
2. Formula 1
Find the sqaure of a number between 25 and 50.
Firstly, 50 subtracts the number to get a result and square it for the last two digits for the square of the number.
Secondly, the number subtracts 25 to get a result for the first two digits of the square of the number.
eg. Find the square of 43.
50 - 43 = 7
72=49
Thus, 49 is the last two digits for the square of 43.
43 - 25 = 18
Thus, 18 is the first two digits for the square of 43.
Finally, the square of 43 is 1849.

Find the square of 36.
50 - 36 = 14
142=196
Thus, 96 is the last two digits for the square of 36.(the "1" is left for next step)
36 - 25 = 11
Thus, the first two digits for the square of 36 is 11+1=12
Finally, the square of 36 is 1296.

3. Formula 2
Find the square of a number between 50 and 75.
Firstly, the number subtracts 50 to get a result and square it for the last two digits for the square of the number.
Secondly, the number subtracts 25 to a result for the first two digits of the square of the number.
eg. Find the square of 58.
58 - 50 = 8
82=64
Thus, the last two digits for the square of 58 is 64.
58 - 25 = 33
Thus, the first two digits for the square of 58 is 33.
Finally, the square of 58 is 3364.

Find the square of 67.
67 - 50 = 17
172=289
Thus, the last two digits for the square of 67 is 89. (the "2" is left for next step)
67 - 25 = 42
Thus, the first two digits for the sqaure of 67 is 42+2=44.
Finally, the square of 67 is 4489.

4. Formula 3
Find the square of a number between 75 and 100.
Firstly, 100 subtracts the number to get a result and square it for the last two digits for the square of the number.
Secondly, the number subtracts the result to get a new result for the first two digits for the square of the number.

eg. Find the square of 97.
100 - 97 = 3
32=9
Thus, the last two digits for the square of 97 is 09.
97 - 3 = 94
Thus, the first two digits for the square of 97 is 94.
Finally, the square of 97 is 9409.

Find the square of 87.
100 - 87 = 13
132=169
Thus, the last two digits for the square of 87 is 69. (the "1" is left for next step)
87 - 13 = 74
Thus, the first two digits for the square of 87 is 74+1=75.
Finally, the square of 87 is 7569

Find The Square Of A More-Than-Two-digit Number
Method: 1. Divide the more than two-digit number into two parts and 
             make the right part have two digits.
          2. Get the square of the left part for the head of the square
             of the number.
          3. Double the product of left and right parts for the two 
             digits follow the head.
          4. Get the square of the right part for the last two digits.

eg1.  Find the square of 123.
1. 123 is divided into two parts, 1(left part) and 23(right part).
2. The square of 1 is 1.(get the head ofthe square of the number)
3. 2 x (1 x 23) = 46.(get two the digits follow the head)
4. The square of 23 is 529.(get the two digits, 29 for the last two digits)
5. 
   1
    46
     529
   -----
 = 15129

eg2.  Find the square of 879.
1. 879 is divided into two parts, 8(left part) and 79(right part).
2. The square of 8 is 64.(get the head)
3. 2 x (8 x 79) = 1264.(get the two digits, 64 follow the head)
4. The square of 79 is 6241.(get the two digits, 41 for the last two digits)
5.
   64
   1264
     6241
   ------
 = 772641

eg3.  Find the square of 1204.
1. 1204 is divided into two parts, 12(left part) and 04(right part).
2. The square of 12 is 144.(get the head)
3. 2 x (12 x 4) = 96.(get the two digits follow the head)
4. The square of 4 is 16.(get the two digits for the last two digits)
5.
   144
      96
        16
   -------
 = 1449616

eg4.  Find the square of 2415.
1. 2415 is divided into two parts, 24(left) and 15(right).
2. The square of 24 is 576.(get the head)
3. 2 x (24 x 15) = 720.(get the two digits, 20 follow the head) 
4. The square of 15 is 225.(get the digits, 25 for the last two digits)
5.
   576
     720
       225
   -------
 = 5832225


eg5.  Find the square of 9758.
1. 9758 is divided into 97 and 58.
2. The square of 97 is 9409.
3. 2 x (97 x 58) = 58 x 2 (100-3) = 11600-348 = 11252.
4. The square of 58 is 3364.
5.
   9409
    11252
       3364
   --------
 = 95218564

Certainly, the number with more digits, the more difficult to find
its square. see next example.
eg6. Find the square of 495673.
1. 495673 is divided into 4956 and 73.
2. Find the square of 4956.
   a) Divide 4956 into 49 and 56.
   b) The square of 49 is 2401.
   c) 2 x (49 x 56) = 2 x (50 - 1) x (50 + 6) = (100 - 2) x (50 + 6)
      = 5000 - 100 + 600 - 12 = 5488.
   d) The square of 56 is 3136.
   e) 2401
        5488
          3136
      --------
    = 24561936

3. 2 x (4956 x 73) = 2 x (5000 - 44) x (70 + 3)
   = (10000 - 88) x (70 + 3)
   = 700000 - 6160 + 30000 - 264
   = 723576

4. The square of 73 is 5329.
5.
   24561936
       723576
           5329
   ------------
 = 245691722929


Find The Square Of A Two-digit Number End With 5
When a two-digit number ends with 5, it is very easy to find its
square. Firstly, the first digit plus 1 and times the first digit
to get the head.  Secondly, paste 25 to follow the head.

eg. Find the square of 35.
1. (3 + 1) x 3 = 12.(get the head)
2. 
    12
      25
    ----
  = 1225

Everything has its own property, Calculus is no exception.



Poem is a way to express one's thought.


The Possession


You come
You finally come
I heard your breath
I see your smile
Just slightly
My everythig belongs to you

Slowly
You come near to me
I forget
     All my precautions
while you are standing in front of me

At the second
     You are ready to kiss me
I could not hold you snugly
I call out tearfully
     ---" No "
I open my eyes unwillingly
     and see the sunshine comes through my window
I lose you
     and my everything



Me


Me, shy as a mimosa
When I contact with strangers
my ears are two pieces of
	irons in fire

I'm a aeolian bell
In a windless greenhouse
it's a dumb
In a winded outdoor
it could sing out a wonderful song

Me, funny as mathematics
Sometimes, it is difficult
	to find the answer out from me

I'm a bateau in Pacific Ocean
I don't know
	where I'll drift
	where should I drift.....



A Real Dream

Dream
In a real dream
i find a real affection
That's ------
	you

The you in my visualazation
The eyes that can talk
It seems to be
	the stars of full of poetic quality
That beats my heart profoundly



Birdie

Birdie
  is brawny
  and never crunches under
		its fate


Birdie
  although it can't fly high
  it can draws the curve of life


Birdie
  is like a bateau
  not afraid of storm
  hangs its hope high on
		its mast
  goes toward the oasis of life


The World

I have many feelings to this world
  	but I don't know how to describe.
  
I have many questions to this world
	but I don't know how to ask.

I have many vexations to this world
	but I don't know how to solve.

I have ...
	but I ...

The world of love
	is vague.
The world of love
	is intricate.



Response


A period of science,
	is talking about the stimulus.
That stabs my heart directly.

An usual afternoon,
An empty seat,
What do I feel?
	Who knows?
But I know that
	I have been avoiding.


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