Pythagorean Independence Day

Today is 15th August 2017. The 70th anniversary of the Independence Day of India. . The date has an interesting property. 15th August 2017 is written as 15/8/17 in India. (It is written as 8/15/17 in American style. But, I am not concerned about that. Nor would that affect the mathematical beauty of the date)

It can be noticed here that in 15/8/17, $15^2+8^2=17^2$ . The triplet is a Pythagorean Triplet.

I had never realized that the Indian Independence Day date has the property of being a part of a Pythagorean Triplet.

Now the question comes : How common or rare are the dates in the calendar which can be part of a Pythagorean Triplet?

As it turns out, they are indeed rare.

There are only 12 dates (dd/mm/yy) which have the property $dd^2+mm^2=yy^2$

04/03/05, 03/04/05, 12/05/13, 08/06/10, 24/07/25, 06/08/10, 15/08/17, 12/09/15, 24/10/26, 05/12/13, 09/12/15, 16/12/20

If one relaxes the condition that $(dd,mm,yy)$ form a pythagorean triplet without the restriction that $yy$ is the largest number in the triplet, 16 additional dates would arise.

05/03/04, 05/04/03, 03/05/04, 04/05/03, 13/05/12, 10/06/08, 25/07/24, 10/08/06, 17/08/15, 15/09/12, 06/10/08, 08/10/06, 26/10/24, 13/12/05, 15/12/09, 20/12/16

Now, my fellow mathematical enthusiasts can see if any of the above dates are relevant to them and spread the word of the speciality of that date

Markdown

Appears as

*italics* or _italics_

italics

**bold** or __bold__

bold


- bulleted
- list

bulleted
list


1. numbered
2. list

numbered
list

Note: you must add a full line of space before and after lists for them to show up correctly

paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)

example link

> This is a quote

This is a quote

    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"

# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"

Math

Appears as

Remember to wrap math in $ ... $ or \[ ... \] to ensure proper formatting.

2 \times 3

2 \times 3

2^{34}

2^{34}

a_{i-1}

a_{i-1}

\frac{2}{3}

\frac{2}{3}

\sqrt{2}

\sqrt{2}

\sum_{i=1}^3

\sum_{i=1}^3

\sin \theta

\sin \theta

\boxed{123}

\boxed{123}

Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
- bulleted - list	bulleted list
1. numbered 2. list	numbered list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1 paragraph 2	paragraph 1 paragraph 2
`[example link](https://brilliant.org)`	example link
`> This is a quote`	This is a quote
# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"	# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

This is awesome!!!!!!!!!!!!!

Sumukh Bansal - 3 years, 6 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$