Class 6 Maths Chapter 1: Patterns in Mathematics (Hinglish Notes)

Maths kya hai?

Maths kaafi had tak patterns ki khoj hai, aur is baat ki ki ve patterns kyun hote hain. Patterns hamare chaaron taraf hain: prakriti mein, ghar aur school mein, sooraj, chaand aur taaron ki chaal mein, aur khareedaari, khaana banaane, gend phenkne, khel, mausam aur technology mein. Patterns dhoondhna mazedaar aur creative ho sakta hai, isiliye mathematicians maths ko art aur science dono maante hain. Pattern kyun hota hai, ye samjhaana utna hi zaroori hai jitna use dhoondhna, kyunki ye samjhaavat bahut door tak kaam aati hai: taaron aur grahon ki chaal ke patterns se gravitation ka siddhaant aur Moon aur Mars tak satellites aur rockets mile, aur genomes ke patterns beemaariyon ki pehchaan aur ilaaj mein madad karte hain.

Number sequences

Whole numbers, 0, 1, 2, 3, 4, …, ke patterns padhne waali shaakha number theory hai, aur number sequences iske sabse buniyaadi patterns hain.

Sequence	Pehle numbers	Niyam
All 1’s	1, 1, 1, 1, …	har number 1
Counting numbers	1, 2, 3, 4, …	1 jodo
Odd numbers	1, 3, 5, 7, …	1 se shuru, 2 jodo
Even numbers	2, 4, 6, 8, …	2 se shuru, 2 jodo
Triangular numbers	1, 3, 6, 10, 15, …	2, phir 3, phir 4, … jodo
Squares	1, 4, 9, 16, 25, …	n × n
Cubes	1, 8, 27, 64, 125, …	n × n × n
Virahānka numbers	1, 2, 3, 5, 8, 13, …	pichhle do numbers jodo
2 ki powers	1, 2, 4, 8, 16, …	2 se guna
3 ki powers	1, 3, 9, 27, 81, …	3 se guna

Aur padho number sequences kya hain mein.

Tasveeron mein sequences

Kai sequences banaaye ja sakte hain. Triangular numbers binduon ke triangle hain, squares binduon ke square grid, aur cubes chhote cubes se bane bade cubes. Ek hi number alag-alag roop le sakta hai: 36 ko 6 × 6 square mein bhi aur 1 se 8 binduon ki rows waale triangle mein bhi jamaaya ja sakta hai. Hexagonal numbers, 1, 7, 19, 37, …, beech ke bindu ke chaaron taraf hexagon banaate hain; agla 61 hai. 2 ki powers bhi banaayi ja sakti hain: ek bindu, do bindu, 4 ka square, 8 ka cube, aur aage. Aur padho triangular aur square numbers mein.

Sequences aapas mein jude hain

Number sequences anokhe tareekon se jude ho sakte hain. Odd numbers jodne pe squares milte hain: 1 = 1, 1 + 3 = 4, 1 + 3 + 5 = 9, 1 + 3 + 5 + 7 = 16. Kyun? Binduon ka square grid 1, 3, 5, 7, … binduon ki L-shaped parton mein baanta ja sakta hai, aur aisi tasveer kisi bhi size ke square ke liye ban sakti hai. Isliye pehle 10 odd numbers ka jod 10 × 10 = 100 hai, aur pehle 100 ka 10,000. Counting numbers ko upar aur phir neeche jodne se bhi squares milte hain: 1 + 2 + 3 + 4 + 3 + 2 + 1 = 16.

Chapter ke aur rishte: counting numbers jodne se triangular numbers milte hain; lagaataar do triangular numbers ka jod square hota hai (10 + 15 = 25); 1 + 2 + 4 + 8 = 15, aur 1 jodne pe 16, yaani 2 ki agli power; triangular number × 6 + 1 se hexagonal number milta hai (6 × 3 + 1 = 19); aur hexagonal numbers jodne se cubes milte hain (1 + 7 + 19 = 27).

Shapes ke patterns

Shapes ke patterns padhne waali shaakha geometry hai. Shapes ek, do ya teen dimensions mein, ya isse bhi zyaada mein ho sakti hain. Chapter ke shape sequences hain regular polygons (triangle, square, pentagon, hexagon, …: barabar bhujaayein aur barabar angles), complete graphs (har bindu baaki har bindu se juda), stacked squares, stacked triangles aur Koch snowflake. Aur padho shapes mein patterns mein.

Shapes aur numbers ka milna

Shape sequence	Kya ginte hain	Number sequence
Regular polygons	bhujaayein (ya kone)	3, 4, 5, 6, … (3 se counting numbers)
Complete graphs	lines	1, 3, 6, 10, 15, … (triangular numbers)
Stacked squares	chhote squares	1, 4, 9, 16, … (squares)
Stacked triangles	chhote triangles	1, 4, 9, 16, … (squares)
Koch snowflake	line segments	3, 12, 48, 192, … (3 × 4 ki powers)

Har Figure it Out sawal ka jawab Chapter 1 ke NCERT solutions mein hai.