O slideshow foi denunciado.
Utilizamos seu perfil e dados de atividades no LinkedIn para personalizar e exibir anúncios mais relevantes. Altere suas preferências de anúncios quando desejar.
Próximos SlideShares
Carregando em…5
×

# Cell division and pascal triangle

7.891 visualizações

Incluce real life examples of pascal triangle

• Full Name
Comment goes here.

Are you sure you want to Yes No
Your message goes here
• Uterine Fibroids Cure, Discover How To Reverse And Rid, All Uterine Fibroids In 2 Months  https://tinyurl.com/rbqozdv

Tem certeza que deseja  Sim  Não
Insira sua mensagem aqui

Tem certeza que deseja  Sim  Não
Insira sua mensagem aqui

### Cell division and pascal triangle

1. 1. CELL DIVISION AND PASCAL TRIANGLE
2. 2. Pascal triangle • Pascal's triangle is a number triangle with numbers arranged in staggered rows. • Pascal triangle is the ideal law of cell division
3. 3. History • Named after Blaise Pascal, the official founder of this mathematical device. • In Italy, Pascal's Triangle is actually known as Tartaglia's Triangle, named after Niccolo FontanaTartaglia, a famous • Befor pascal the numbers originated in the Hindu religion in India by omar khyyam and it was also discovered by the Chinese in the 13th century.
4. 4. Chinese version of pascal triangle • The Chinese’s version of the Pascal’s triangle was found in Chu Shi-Chieh's book "Ssu Yuan Yü Chien" (Precious Mirror of the Four Elements), written in AD 1303 which is more than 700 years ago and also more than 300 years before Pascal discovered it. The book also mentioned that the triangle was known about more than two centuries before that.
5. 5. Property of Pascal triangle • Sum of rows is the nth power of 2. i.e. 2^n
6. 6. Binomial expansion • (푎 + 푏)2= 푎2 + 2푎푏 + 푏2
7. 7. Fibonacci numbers • The Fibonacci numbers can be found by adding up angles from certain ones to ones.
8. 8. Cell division • Cell division involves the distribution of identical genetic material, DNA, to two daughters cells. There are two types of cell divison. • Mitosis • Meiosis
9. 9. Mitosis • Mitosis is a fundamental process for life. • During mitosis, a cell duplicates all of its contents, including its chromosomes, and splits to form two identical daughter cells. • the steps of mitosis are carefully controlled by a number of genes. When mitosis is not regulated correctly, health problems such as cancer can result.
10. 10. REALTION OF PASCAL TRIANGLE WITH MITOSIS
11. 11. Relation with nth power of 2 • In cycle 1, there is a cell-creator: 1 A0 • In cycle2, our mother cell A0 during the mitosis duplicates into two daughter cells: 2 A1
12. 12. • So in cycle 3, the two mother cells, 2 A1, duplicate into four daughter cells: 4 A2 • In cycle 4 the four mother cells, 4 A2, during the mitosis duplicate into eight daughter cells: 8 A3; • In cycle n, the 2n-2 An-2 mother cells, duplicate into 2n-1 daughter cells: 2n-1 An-1 .
13. 13. • The number sequence which represents the cell division is a geometrical series: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512…… We know that this type of sequence exist in Pascal triangle as we discussed above.
14. 14. Relation with binomial expansion • in cycle 1, our young cell becomes a mother for the first time and produces her first daughter cell: A0 + A1 • In cycle 2, the mother cell A0 reproduces into A0 + A1, as well as cell-daughter reproduces into A1 + A2 . Now, three generations are present: A0 + 2 A1 + A2.
15. 15. • In cycle 3, the original mother cell produces another daughter cell. Two mother cells A1 reproduce into 2 A1 + 2 A2. The mother cell A2 also produces its own daughter cell. Now four generations are present:A0 + 3 A1 + 3 A2 + A3 ; • In cycle 4, there are: A0 + 4 A1 + 6 A2 + 4 A3 + A4; • In cycle 5, there are: A0 + 5 A1 + 10 A2 + 10 A3 + 5 A4 + A5.
16. 16. • The number of cell in each cycle produces the rows of pascal triangle. 1A0 1A0 1A1 1A0 2A1 1A2 1A0 3 A1 3A2 1A3 1A0 4A1 6A2 4A3 1A4 1A0 5A1 10A2 10A3 5A4 1A5
17. 17. Other examples of Pascal triangle • Electronic configuration and second kind of Pascal triangle • Architecture-lost in Pascal triangle • Nature-Fibonacci numbers
18. 18. Second kind of Pascal triangle
19. 19. Electronic configuration and Second kind of Pascal triangle
20. 20. Electronic configuration • An electron configuration is a method of indicating the arrangement of electrons about a nucleus. A typical electron configuration consists of numbers, letters and superscripts with the following format: • A number indicates the energy level.( The number is called the principal quantum number.) • A letter indicates the type of orbital: s,p,d,f... • A superscript indicates the number of electrons in the orbital.
21. 21. Relation • The maximum number of electrons is double square number. The square numbers can be found in the second kind of triangle 1 1 2 1 3 2 1 4 5 2 1 5 9 7 2 1 6 14 16 9 2 1 7 20 30 25 11 2 1 8 27 50 55 36 13 2 1 9 35 77 105 91 49 15 2
22. 22. Relation • Electronic shells actually have sublevels, i.e. s, p, d, f… number of orbitals in each sublevels are 1, 3, 5, 7, 9,..... respectively. 1 1 2 1 3 2 1 4 5 2 1 5 9 7 2 1 6 14 16 9 2 1 7 20 30 25 11 2 1 8 27 50 55 36 13 2 1 9 35 77 105 91 49 15 2
23. 23. Architecture • Shanghai-based multidisciplinary design company super nature design has developed 'lost in pascal's triangle'. • 100 triangular LED lights • Xylophone triangles
24. 24. Fibonacci numbers in nature • The Fibonacci numbers play a significant role in Nature. Many plants show the Fibonacci numbers in the arrangements of the leaves around their stems. • One estimate is that 90 percent of all plants exhibit this pattern of leaves involving the Fibonacci numbers. • E.g in grasses, rose, apple etc