Upside Down Magic, Bimagic, Palindromic Squares and Pythagoras Theorem on a Palindromic Day - 11.02.2011

TL;DR

This paper constructs various upside down, bimagic, and palindromic squares based on the palindromic date 11.02.2011, demonstrating their mathematical properties and relations to Pythagoras theorem using only digits 0, 1, and 2.

Contribution

It introduces new upside down bimagic and palindromic squares derived from a specific palindromic date, exploring their properties and connections to classical theorems.

Findings

Magic sums satisfy Pythagoras theorem

Bimagic squares of various orders are constructed

Some squares are palindromic and upside down

Abstract

In this short paper we have produced different kinds of upside down magic squares based on a palindromic day 11.02.2011. In this day appear only the algorisms 0, 1 and 2. Some of the magic squares are bimagic and some are palindromic. Magic sums of the magic squares of order 3x3, 4x4 and 5x5 satisfies the Pythagoras theorem. Bimagic squares of order 9x9 are produced with 4, 6 and 8 digits. The bimagic square of order 9x9 with 8 digits is of palindromic numbers. We have given bimagic squares of order 16x16 and 25x25, where the magic sum S1 in both the cases is same. In order to make these magic squares upside down, i.e., 180 degrees rotation, we have used the numbers in the digital form. All these magic square are only with three digits, 0, 1 and 2 appearing in the day 11.02.2011.