ENTERESAN SAYILAR
Pi Sayısının Hikayesi


Kısaca bir dairenin çevresinin çapına oranı, p sayısını verir. İnsanoğlu, aslında çok önemli vazifeleri olan bu sayı üzerinde çok düşünmüştür. Yıllarca tam olarak bir değer bulamamakla beraber, gerçek değerine en yakın sonuçları kullanabilmek için çaba sarfetmişlerdir.


p' nin kronolojik gelişimine baktığımızda günümüzde dahi tam bir sonuç bulunamamıştır. Çeşitli formüller üretilmesine rağmen sadece her seferinde gerçek değere biraz daha yaklaşılmıştır.


Arşimet 3.1/7 ile 3.10/71 arasında bir sayı olarak hesapladı. Mısırlılar 3.1605, Babilliler 3.1/8, Batlamyus 3.14166 olarak kullandı. İtalyan Lazzarini 3.1415929, Fibonacci ise 3.141818 ile işlem yapıyordu. 18.yyda 140, 19yyda 500 basamağa kadar hesaplandı. İlk bilgisayarlarla 2035 basamağı hesaplanırken günümüzde milyonlarca basamağa kadar çıkılıyor. İşin ilginç tarafı, hâlâ tam bir sonuç yok. Herhangi bir yerinde devir olsa iş yine kolaylaşacak. Ama henüz öyle bir şeye de rastlanmadı. Şu anda bilinen değerden birkaç basamak:


pi=3,1415926535897932384626433832795028841


971693993751058209749445923078164062862089


986280348253421170679821480865132823066470


938446095505822317253594081284811174502841027.....



ENTERESAN SAYILAR


Üç basamaklı herhangi bir sayıyı iki kere yanyana yazarak elde ettiğimiz yeni sayı, kesinlikle 7, 11, 13, 77, 91, 143, 1001 sayılarına kalansız olarak bölünür(neden?).


Örnek: 831831


831831 / 7 = 118833
831831 / 11 = 75621
831831 / 13 = 63987
831831 / 77 = 10803
831831 / 91 = 9141
831831 / 143 = 5817
831831 / 1001 = 831

Sihirli Kareler:
3 x 3: Birbirini yatay, dikey ve çapraz takip eden üç karenin toplamı, 15.
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8</TD>
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1</TD>
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6</TD></TR>
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3</TD>
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5</TD>
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7</TD></TR>
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4</TD>
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9</TD>
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2</TD></TR></T></TABLE>
4 x 4: Birbirini yatay, dikey ve çapraz takip eden dört karenin toplamı, 34.
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16</TD>
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2</TD>
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3</TD>
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13</TD></TR>
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5</TD>
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11</TD>
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10</TD>
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8</TD></TR>
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9</TD>
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7</TD>
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6</TD>
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12</TD></TR>
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4</TD>
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14</TD>
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15</TD>
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1</TD></TR></T></TABLE>
5 x 5: Birbirini yatay, dikey ve çapraz takip eden beş karenin toplamı, 65.
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3</TD>
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16</TD>
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9</TD>
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22</TD>
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15</TD></TR>
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20</TD>
<TD style="BORDER-RIGHT: black 1pt inset; PADDING-RIGHT: 0.75pt; BORDER-TOP: black 1pt inset; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: black 1pt inset; WIDTH: 15pt; PADDING-TOP: 0.75pt; BORDER-BOTTOM: black 1pt inset; HEIGHT: 15.75pt" width=20>
8</TD>
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21</TD>
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14</TD>
<TD style="BORDER-RIGHT: black 1pt inset; PADDING-RIGHT: 0.75pt; BORDER-TOP: black 1pt inset; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: black 1pt inset; WIDTH: 15pt; PADDING-TOP: 0.75pt; BORDER-BOTTOM: black 1pt inset; HEIGHT: 15.75pt" width=20>
2</TD></TR>
<TR style="HEIGHT: 15.75pt">
<TD style="BORDER-RIGHT: black 1pt inset; PADDING-RIGHT: 0.75pt; BORDER-TOP: black 1pt inset; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: black 1pt inset; WIDTH: 15pt; PADDING-TOP: 0.75pt; BORDER-BOTTOM: black 1pt inset; HEIGHT: 15.75pt" width=20>
7</TD>
<TD style="BORDER-RIGHT: black 1pt inset; PADDING-RIGHT: 0.75pt; BORDER-TOP: black 1pt inset; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: black 1pt inset; WIDTH: 15pt; PADDING-TOP: 0.75pt; BORDER-BOTTOM: black 1pt inset; HEIGHT: 15.75pt" width=20>
25</TD>
<TD style="BORDER-RIGHT: black 1pt inset; PADDING-RIGHT: 0.75pt; BORDER-TOP: black 1pt inset; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: black 1pt inset; WIDTH: 15pt; PADDING-TOP: 0.75pt; BORDER-BOTTOM: black 1pt inset; HEIGHT: 15.75pt" width=20>
13</TD>
<TD style="BORDER-RIGHT: black 1pt inset; PADDING-RIGHT: 0.75pt; BORDER-TOP: black 1pt inset; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: black 1pt inset; WIDTH: 15pt; PADDING-TOP: 0.75pt; BORDER-BOTTOM: black 1pt inset; HEIGHT: 15.75pt" width=20>
1</TD>
<TD style="BORDER-RIGHT: black 1pt inset; PADDING-RIGHT: 0.75pt; BORDER-TOP: black 1pt inset; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: black 1pt inset; WIDTH: 15pt; PADDING-TOP: 0.75pt; BORDER-BOTTOM: black 1pt inset; HEIGHT: 15.75pt" width=20>
19</TD></TR>
<TR style="HEIGHT: 15.75pt">
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24</TD>
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12</TD>
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5</TD>
<TD style="BORDER-RIGHT: black 1pt inset; PADDING-RIGHT: 0.75pt; BORDER-TOP: black 1pt inset; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: black 1pt inset; WIDTH: 15pt; PADDING-TOP: 0.75pt; BORDER-BOTTOM: black 1pt inset; HEIGHT: 15.75pt" width=20>
18</TD>
<TD style="BORDER-RIGHT: black 1pt inset; PADDING-RIGHT: 0.75pt; BORDER-TOP: black 1pt inset; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: black 1pt inset; WIDTH: 15pt; PADDING-TOP: 0.75pt; BORDER-BOTTOM: black 1pt inset; HEIGHT: 15.75pt" width=20>
6</TD></TR>
<TR style="HEIGHT: 15.75pt">
<TD style="BORDER-RIGHT: black 1pt inset; PADDING-RIGHT: 0.75pt; BORDER-TOP: black 1pt inset; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: black 1pt inset; WIDTH: 15pt; PADDING-TOP: 0.75pt; BORDER-BOTTOM: black 1pt inset; HEIGHT: 15.75pt" width=20>
11</TD>
<TD style="BORDER-RIGHT: black 1pt inset; PADDING-RIGHT: 0.75pt; BORDER-TOP: black 1pt inset; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: black 1pt inset; WIDTH: 15pt; PADDING-TOP: 0.75pt; BORDER-BOTTOM: black 1pt inset; HEIGHT: 15.75pt" width=20>
4</TD>
<TD style="BORDER-RIGHT: black 1pt inset; PADDING-RIGHT: 0.75pt; BORDER-TOP: black 1pt inset; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: black 1pt inset; WIDTH: 15pt; PADDING-TOP: 0.75pt; BORDER-BOTTOM: black 1pt inset; HEIGHT: 15.75pt" width=20>
17</TD>
<TD style="BORDER-RIGHT: black 1pt inset; PADDING-RIGHT: 0.75pt; BORDER-TOP: black 1pt inset; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: black 1pt inset; WIDTH: 15pt; PADDING-TOP: 0.75pt; BORDER-BOTTOM: black 1pt inset; HEIGHT: 15.75pt" width=20>
10</TD>
<TD style="BORDER-RIGHT: black 1pt inset; PADDING-RIGHT: 0.75pt; BORDER-TOP: black 1pt inset; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: black 1pt inset; WIDTH: 15pt; PADDING-TOP: 0.75pt; BORDER-BOTTOM: black 1pt inset; HEIGHT: 15.75pt" width=20>
23</TD></TR></T></TABLE>

İlginç Sayılar(3):
1 x 8 + 1 = 9
12 x 8 + 2 = 98
123 x 8 + 3 = 987
1234 x 8 + 4 = 9876
12345 x 8 + 5 = 98765
123456 x 8 + 6 = 987654
1234567 x 8 + 7 = 9876543
12345678 x 8 + 8 = 98765432
123456789 x 8 + 9 = 987654321



Teorem:


Bütün kare sayılar, 1'den başlamak üzere sırasıyla tek tamsayıların toplamı olarak yazılabilir.


Örnekler:
5²=25
1 + 3 + 5 + 7 + 9 = 25
11² = 121
1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 = 121



Üçgen Sayılar:


1'den başlamak üzere kendisinden önceki tüm sayıların toplamına karşılık gelen sayıların dizisidir.


1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, ... pozitif doğal sayılar ise, üçgen sayılar:


1, 3(1+2), 6(1+2+3), 10(1+2+3+4), 15(1+2+3+4+5),... üçgen sayılardır. Yani:


1, 3, 6, 10, 15, 21, 28, 36, 45, 55...