Mathematics Village

·          Draw a Quadrilateral ABCD on colour chart Sheet . ·          Cut such four Quadrilaterals on four different sheets. ·          Mark Ð A as Ð 1 ,   Ð B as Ð 2 , Ð C as Ð 3 and Ð D as Ð 4 on each quadrilateral as shown in fig . ·          Arrange all four angles of quadrilateral one from each colour at one point. ·          What you observe ? ·          It forms a complete angle i.e 360 0 ·          This shows that sum of all angles of quadrilateral is 360 0    

Squaring   Let us take advantage of   algebraic identity. A 2 = ( A - d )( A + d ) + d 2 Naturally, this formula works for any value of d , but we should choose d to be the distance to a number close to A that is easy to multiply. Examples. To square the number 23, we let d = 3 to get 23 2 = 20 x 26 + 3 2 = 520 + 9 = 529 :   To square 48, let d = 2 to get 48 2 = 50 x 46 + 2 2 = 2300 + 4 = 2304 :   With just a little practice, it's possible to square any two-digit number in a matter of seconds. Once you have mastered those, we can quickly square three-digit numbers by rounding up and down to the nearest hundred. Examples. 223 2 = 200 x 246 + 23 2 = 49 ; 200 + 529 = 49 ; 729 952 2 = 1000 x 904 + 48 2 = 904 ; 000 + 2 ; 304 = 906 ; 304 : To do mental calculations of this size, one needs to be quick at multiplying 2-digit and 3-digit numbers by 1-digit numbers, generating the answer from left to right.  

The tangram   is a dissection puzzle consisting of seven flat shapes, called tans, which are put together to form shapes. The objective of the puzzle is to form a specific shape (given only an outline or silhouette) using all seven pieces, which may not overlap. It was originally invented in China at some unknown point in history, and then carried over to Europe by trading ships in the early 19th century. It became very popular in Europe for a time then, and then again during World War I. It is one of the most popular dissection puzzles in the world.[ Over 6500 different tangram problems have been compiled from 19th century texts alone, and the current number is ever-growing. The number is finite, however. Fu Traing Wang and Chuan-Chin Hsiung proved in 1942 that there are only thirteen convex tangram configurations (configurations such that a line segment drawn between any two points on the configuration's edge always pass through the configuration's interior, i.e., conf...

Multiplication of two numbers that differ by 2 Note :This trick only works if you know the squares of numbers.   When two numbers differ by 2, their product is always the square of the number in between these numbers minus 1. 12 x 14 =    (13 x 13)   - 1 =  169 - 1 =  168   18 x 20 =   (19 x 19)   - 1 =  361 - 1 =  360 25 x 27 =   (26 x26)   - 1 =  676 - 1 =  675   13 x 15 =   (14 x 14)   - 1 =  196 - 1 =  195 15 x 17 =   (16 x 16)   - 1 =  256 - 1 =  255 16 x 18 =   (17 x 17)   - 1 =  289 - 1 =  288        

 

Ekādhikena Pūrvena , ("By one more than the previous one") This  sūtra means that the prescribed arithmetical operation is either multiplication or division. Both are implied since we may proceed leftward and multiply (and carry-over the excess value to the next leftward column) or we may go rightward and divide (while prefixing the remainder). When dividing by a nine's family denominator, the digit to the left of the nine (previous) is increased by one to obtain the multiplier. .Examples: 35×35 = ((3×3)+3),25 = 12,25 and 125×125 = ((12×12)+12),25 = 156,25   or by the sūtra, multiply "by one more than the previous one." 35×35 = ((3×4),25 = 12,25 and 125×125 = ((12×13),25 = 156,25   The latter portion is multiplied by itself (5 by 5) and the previous portion is square of first digit or first two digit (3×3) or (12×12) and adding the same digit in that figure (3or12) resulting in the answer 1225. (Proof) This is a simple application of   when and ...