Mathematics Village

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 ...

This list of sutras is taken from the book Vedic Mathematics, which includes a full list of the sixteen Sutras in Sanskrit, The Main Sutras 1.        By one more than the one before. 2.        All from 9 and the last from 10. 3.        Vertically and Cross-wise 4.        Transpose and Apply 5.        If the Samuccaya is the Same it is Zero 6.        If One is in Ratio the Other is Zero 7.        By Addition and by Subtraction 8.        By the Completion or Non-Completion 9.        Differential Calculus 10.     By the Deficiency 11.     Specific and General 12.     The Remainders by the Last Digit ...

For this example we will use 25 Take the "tens" part of the number (the 2 and add 1)=3 Multiply the original "tens" part of the number by the new number (2x3) Take the result (2x3=6) and put 25 behind it. Result the answer 625. Square of 35 Take the "tens" part of the number (the 3 and add 1)=4 Multiply the original "tens" part of the number by the new number (3x4) Take the result (3x4=12) and put 25 behind it. Result the answer 1225. Square of 75 Take the "tens" part of the number (the 7 and add 1)=8 Multiply the original "tens" part of the number by the new number (7x8) Take the result (7x8=56) and put 25 behind it. Result the answer 5625.