First ever 4 × 4 Magic Square (Chautīsā Yantra)

Transcript

First ever 4 × 4 Magic Square (Chautīsā Yantra) The first ever recorded 4 × 4 magic square is found in a 10th century inscription at the Pārśhvanath Jain temple in Khajuraho, India, and is known as the Chautīsā Yantra Chau̐tīs means 34 Here, Sum of all rows is 34 16 + 09 + 04 + 05 = 34 03 + 06 + 15 + 10 = 34 13 + 12 + 01 + 08 = 34 02 + 07 + 14 + 11 = 34 Sum of all columns is 34 16 + 03 + 13 + 02 = 34 09 + 06 + 12 + 07 = 34 04 + 15 + 01 + 14 = 34 05 + 10 + 08 + 11 = 34 Sum of Diagonals is 34 16 + 06 + 01 + 11 = 34 05 + 15 + 12 + 02 = 34 Sum of Corners of 2 × 2 sub-squares 16 + 09 + 06 + 03 = 34 09 + 04 + 15 + 06 = 34 04 + 05 + 10 + 15 = 34 03 + 06 + 12 + 13 = 34 06 + 15 + 01 + 12 = 34 15 + 10 + 08 + 01 = 34 13 + 12 + 07 + 02 = 34 12 + 01 + 14 + 07 = 34 01 + 08 + 11 + 14 = 34 Sum of Corners of 3 × 3 sub-squares 16 + 04 + 01 + 13 = 34 09 + 05 + 08 + 12 = 34 03 + 15 + 14 + 02 = 34 06 + 10 + 11 + 07 = 34 Sum of Corners of the 4 × 4 full-square 16 + 05 + 11 + 02 = 34 Sum of Corners of vertical rectangles 16 + 09 + 07 + 02 = 34 09 + 04 + 14 + 07 = 34 04 + 05 + 11 + 14 = 34 Sum of Corners of horizontal rectangles 16 + 05 + 10 + 03 = 34 03 + 10 + 08 + 13 = 34 13 + 08 + 11 + 02 = 34 Sum of Corners of inclined rectangles 04 + 10 + 07 + 13 = 34 03 + 09 + 08 + 14 = 34