This work brings representations of 2023 in different ways. These representations are of crazy-type, running numbers, single digit, single letter, Triangular, Fibonacci, palindromic-type, prime numbers, embedded, repeated digits, colored patterns, magic squares, patterned designs, etc. This year the number 23 is a prime number. Let’s call it prime year. Below is a link of work for download:Inder J. … Continue reading 23 and 2023 in Numbers and Patterns

# Category: Curiosities

# Magic Square of Order 40 With 22

Below is a a magic square of order 40 made from consecutive number 1 to 1600. It contains 16 equal sums bordered magic squares of order 8 and 36 equal sums pandiagonal magic squares of order 4. If we consider 16 pandiagonal magic squares of order 4 appearing in 16 bordered magic squares of order 8, then there are 52 pandiagonal magic squares of order … Continue reading Magic Square of Order 40 With 22

# Mathematical Beauty of 2022

This work brings representations of 2022 in different ways. These representations are of crazy-type, running numbers, single digit, single letter, Triangular, Fibonacci, palindromic-type, prime numbers, embedded, repeated digits, colored patterns, magic squares, patterned designs, etc. Interesting, this year there will be a day with 11 times repetition of single digit. It will happens on: 22h … Continue reading Mathematical Beauty of 2022

# Hardy-Ramanujan Number – 1729: Revised

This paper brings representations of 1729, a famous Hardy-Ramanujan number in different situations. These representations are of crazy-type, single digit, single letter, Selfie-type, running expressions, selfie fractions, equivalent fractions, Triangular, Fibonacci, fixed digits repetitions prime numbers patterns , Pythagorean triples, palindromic-type, polygonal-type, prime numbers, embedded, repeated, etc. Ideas toward magic squares are also extended. Some … Continue reading Hardy-Ramanujan Number – 1729: Revised

# Three Digit’s Days of December 2021 – Magic Square of Order Nine With Eights Days

References Inder J. Taneja, Magic Squares, https://inderjtaneja.com/2019/06/27/publications-magic-squares/

# Three Digits Embedded Prime Patterns for Three Days: 20.10.2021, 21.10.2021 and 22.10.2021

References: I.J. TANEJA, Embedded Palindromic Prime Numbers – I, RGMIA Research Report Collection, 20(2017), Art. 121, pp. 1-86, http://rgmia.org/papers/v20/v20a121.pdf.I.J. TANEJA, Palindromic Prime Embedded Trees, RGMIA Research Report Collection, 20(2017), Art. 124, pp. 1-14, http://rgmia.org/papers/v20/v20a124.pdf.Inder J. Taneja, https://inderjtaneja.com/2018/08/16/embedded-palprimes-with-10-palindromic-days-of-august-18/.

# 101st Death Aniversary of Great Mathematican S. Ramanujan: 26.04.1920 – 26.04.1921

References: Inder J. Taneja https://www.researchgate.net/publication/313143468_Hardy-Ramanujan_Number_-1729 (more than 4000 reads);Inder J. Taneja, https://www.researchgate.net/publication/316997853_Numbers_from_1_to_1729_Written_in_Terms_of_1729-1729

# Different Digits Magic Squares of Orders 4, 5, 7 and 8 With 4321: Special on Date – 4.3.21

References: Inder J. Taneja, Multi-Digits Magic Squares, RGMIA Research Report Collection, 18(2015), Art. 159, pp. 1-22, http://rgmia.org/papers/v18/v18a159.pdf. Inder J. Taneja, Different Digits Magic Squares and Number Patterns, Zenodo, February 1, 2019, pp. 1-34, http://doi.org/10.5281/zenodo.2555327.

# Palindromic Day – 12.02.2021: Upside-Down Magic Square of Order 9

References: Inder J. Taneja, Universal Palindromic Day and Two Digits Magic Squares, February 2, 2020, pp. 1-22, Zenodo, http://doi.org/10.5281/zenodo.3633852Inder J. Taneja, 2-Digits Universal and Upside-Down Palindromic Magic and Bimagic Squares: Orders 3 to 16, Zenodo, April 07, 2020, pp. 1-103, http://doi.org/10.5281/zenodo.3743362.

# 21st Day, 21st Year and 21st Century: Upside-Down Semi-Magic Squares of Order 21 With Digits 2 and 1

Semi-Magic Squares of Order 21 With Digits 2 and 1 Above two magic square are semi-magic squares with locks of orders 3 and 7. The semi-magic sums of semi-magic squares is 35555555552. Instead of semi-magic we can construct magic square also, but in this it will be without blocks. Morever, the above magic squares are … Continue reading 21st Day, 21st Year and 21st Century: Upside-Down Semi-Magic Squares of Order 21 With Digits 2 and 1

# More on 2021

Reference: Inder J. Taneja, 21 Mathematical Highlights for 2021, https://inderjtaneja.com/2020/12/28/21-mathematical-hightlights-for-2021/

# 21 Mathematical Hightlights for 2021

This short work brings 21 main representations of 2021 in different ways. These representations are of crazy-type, running numbers, single digit, single letter, Triangular, Fibonacci, palindromic-type, prime numbers, embedded, repeated digits, colored patterns, magic squares, etc. For download this work please go to following link: Inder J. Taneja, 21 Mathematical Highlights for 2021, Zenodo, December … Continue reading 21 Mathematical Hightlights for 2021

# Extended Colored Patterns With 2021 On a Board of 9×9

This work is continuation of work on 2021 given at the following link: Inder J. Taneja, Colored Patterns With 2021 On a Board of 9×9, https://inderjtaneja.com/2020/12/26/colored-pattern-with-2021-on-a-board-of-9x9/ In this work we consider the same designs and put them as blocks of 9x9 (for designs) and 81x81 for small squares. The designs are symmetric as 90o and 180o … Continue reading Extended Colored Patterns With 2021 On a Board of 9×9

# Colored Patterns With 2021 On a Board of 9×9

W E L C O M E - 2021

# Bordered Magic Squares of Orders 13 and 19 With Sums 1729 – Special on Ramanujan’s Day 22.12

Reference: Inder J. Taneja, Hardy-Ramanujan Number -1729, https://www.researchgate.net/publication/313143468_Hardy-Ramanujan_Number_-1729

# Special On Ramanujan’s Day – 22.12: Bordered Magic Square of Order 7 with Ramanujan’s Number 1729

Reference: Inder J. Taneja, Hardy-Ramanujan Number -1729, https://www.researchgate.net/publication/313143468_Hardy-Ramanujan_Number_-1729

# PUZZLE: Alternate Colors Symmetric Patterns 2021

Welcome 2021: Mathematical Style Below are few symmetric patterns made on the board of 9x9. These patterns are with two colors put in an alternate positions. One color numbering 20 and another 21, welcoming 2021. Since these are made manually, there is great chance of repetitions. Below are only 76 patterns, but there are much … Continue reading PUZZLE: Alternate Colors Symmetric Patterns 2021

# Factorial-Type Numerical Calendar

This short work brings factorial-type numerical representations of the Calendar. It is based on a functional equationa of two and three variables representing day, month and year. There are three ways os wring using either 5!, 6! or 8!. It is given for the years ending in 20 and 2020. The other years can be … Continue reading Factorial-Type Numerical Calendar

# First of Twelve: Six Twenties

# 2020 In Numbers – Mathematical Style

Below are some representations of 2020 in terms of numbers and embedded or bordered magic squares. For the full work see the following link: Inder J. Taneja, 2020 In Numbers: Mathematical Style - Revised, Zenodo, December 31, 2019, pp.1-37, http://doi.org/10.5281/zenodo.3596193 The work also appeared in Alex Bellos's column on puzzles in "The Guardian", 30 december, … Continue reading 2020 In Numbers – Mathematical Style