What are some mind-blowing facts about mathematics?

What are some mind-blowing facts about mathematics? by Sandipan Bala

Answer by Sandipan Bala:

Well ever wondered how the Surface Area of a Sphere was derived?

Well here is a great visualisation to alter your perception.

Step 1: Cut the sphere in the following way.

Step 2: Spread the cut out part across the paper

Step 3: Collate the pieces together in the following way

Step 4: Spread the areas out separately to form a sine curve

Step 5: The area of the sine curve is the surface area of the sphere

Here’s a GIF file for better understanding.

There’s of course the generic method of calculation where the surface area is calculated by cutting the sphere into infinitesimally thin disks of varying radius stacked over one another and integrating them, but this above method is a different way to look at the same problem.

Image Source: Google Images

Edit: Updated the images corresponding to the GIF file, since GIF file is not accessible on Quora for mobile devices.

What are some mind-blowing facts about mathematics?

What are some interesting mathematics facts?

What are some interesting mathematics facts? by Sayantan Mahato

Answer by Sayantan Mahato:

The Illegal Number That Shouldn't Exist (And can probably land you in jail)

Yes, there's exists a number like that.

And it has the potential to make the police arrest you.

But sadly (and fortunately), it is a 1401-digit number.

Among the various weird and wacky laws such as — In Russia, Vladimir Putin just recently made it illegal to tell kids that gay people exist.

Here's one which surprisingly is both wacky and logical at the same time.

And if the idea of existence of such a number doesn't already make you wonder how, then the next line is certainly for you:

It's used to prevent sharing of illegal files and documents.

How it came to this?

In the early years of the previous decade (around 2000s), before the coming of streaming services like Netflix, most of the video content was consumed via DVDs. But companies had to be careful with that as people often tried to copy the content to their own DVDs and making plagiarised copy of the original content. So when the plagiarised content, for obvious reasons of being lesser priced started circulating in the market, this led to huge losses in studios revenue. They somehow had to get ahead of those indulged in this act of piracy.

So they started encrypting their content with keys, which were accessible to only the specific user which locked down the content to the DVDs so that they couldn't get copied. And somehow in the midst of this, companies also started suing people because of the copyright infringement and was a very big blow to the pirates.

But, they weren't far behind too. Tools and programs started appearing that could potentially circumvent and bypass these DVD's copyright protection and make bootleg copies of the original content. And somehow, the companies made it illegal for indulging any such activity of circumventing as well lobbied very hard to get the code off the charts and were pretty much successful at that too.

Until again, the pirates gave them another blow.

Remember that computers don't understand human language? They only understand in the form of zeroes and ones. It follows a binary language.

And going by this rule: almost any program could be represented in the form of numbers.

Now if you think that's just plain insane, then you have underestimated the power of internet and its netizens.

Phil Carmondy in 2001, was able to generate a prime number which was basically the binary representation of the program. The number actually was a compressed version of the C program that was able to circumvent and bypass these copyrights!

So basically: he was able to find a number which could replicate all the workings of the program that was used to circumvent the DVD's copyrights.

It is important that what he found was an illegal prime number. And if you are into networking and IT, you must have the idea of importance of prime numbers.

Basically, it is rampantly used across the internet for encryptions decryption purposes. The basic logic being this: its easy to get it from one way but not the other.

Two prime numbers can be multiplied to get a composite number. But a composite number cannot be easily factorised to its prime factors. And just in case, we are talking about tens of hundreds of digits. So you can multiple two 1000 digits prime number to get a very big number. But it would take probably years even for a supercomputer to break down that number to the exact couple of prime numbers used to get the product. So these two numbers act as keys which are only known to you which when multiplied get your product which will unlock the content stored.

Encrypted data uses prime numbers with thousands of digits. This is used across payment gateways as well as discussed above as CD Keys to prevent making bootleg copies of content.

Sony even tried to sue couple of hackers who were able to bypass the copyright and even publishing the keys on the internet!

In fact, other hackers went a step ahead. They converted the binary code into a hexadecimal code. And in case you don't know, hexadecimal code is used to represent colors on the webpages over Internet. So basically the keys were converted into images!

More or less like this:

The more you try to understand the Internet, the lesser will you ever understand about it!

Coming to the main topic, it was soon made illegal to have the program under any way under the Digital Millennium Act (in US).

Infact, its worth noting that it isn't illegal all over the world. Its primarily banned in US and some other bunch of countries only!

So unless you are actually from the US, your personal security won't be jeopardized (though I'm not sure about extradition laws in your country) for which you can be brought to US and punished.

But only when you can find such a number in the first place.

What are some interesting mathematics facts?

Why do many people today claim that ancient Indian texts contain advanced science?

Why do many people today claim that ancient Indian texts contain advanced science? by Ushnik Das

Answer by Ushnik Das:

Ah… such a sweet yet condescending question.

I’ve been going through a number of books on ancient India these days.

I’ll try my level best to convince your curious soul that these aren’t baseless claims but simple scientific facts. Oh yes, I’ve also tried to provide ‘adequate references’.

I’ve segmented the answer into a number of subtopics written in bold. Under them, you’ll find a weirdly spelled-out sentence, this is the Sanskrit sloka written in English. Under the slokas, you’ll get the source of the same.

Finally you’ll have the meaning of the sloka written in English, of course.

DISCLAIMER:

  • This is going to be a long post with only 1 picture. I didn’t want to crowd the answer with unnecessary pictures.
  • The Sanskrit slokas are just converted into English phonetically correct sentences.

Who goes around whom? Earth vs Sun!

ayam gauh prsnirakramit asadanmataram purah pitaram ca prayantsvah

(Rig veda- 10.189.1)

Moon being the sub-planet of earth, is revolving around its motherly planet earth and earth is revolving around its fatherly planet Sun.

So the sages knew that it’s the earth spinning around the sun and not vice-versa.


Seven colours of Sun light?

sapta tva harito rathe vahanti deva surya soaciksesam vicaksana

(Rig veda 1.50.9)

ava divastarayanti sapta suryasya rasmyah

(Atharva veda 17–10–17–1)

Sun’s seven coloured rays are making a day.

eko-asva vahati sapta namah

(Rig veda 1.164.2)

Sun light is one (white) but called as seven (coloured).

Damn! The sages knew this too!


What’s the speed of light?

taranirvisvadarsato jyotiskrdasi surya visvama bhasi rocanam

(Rig veda 1.50.4)

Sayanacarya’s commentary on the above line during the 14th century AD states that this sloka from Rig veda means…

Sunlight travels 2202 yojanas in half nimisa.

1 yojana = 9.11 miles and 1 full day = 8,10,000 half-nimishas.

So, the speed of light as calculated through this sloka is 1,88,064 miles per second.

Wait, according to latest research the speed comes to be 1,86,300 miles per second.

Therefore, you’ve a minuscule error margin of 0.94%. Smart sages… I'd say.


Many apples had fallen before Newton.

akrsta saktisca mahi taya yat svastham guru svabhimukham svasaktya

akrsyate tatpatativa bhati same samantat kva patatviyam khe

(Siddhanta Shiromani, Bhuvanakosa sloka 6)

Earth has her own attractive power due to which, like a waterfall, every object is attracted to her.

Ah! That’s gravity!


What is the meaning of a ‘healthy’ person?

According to Charaka Samhita:

samadosah samagnisa samadhatu malakriyah

prasannatmendriya manah svastha ityabhidhiyate |

In whom there is a balance of three doshas like vata, pita, kapha; dhathus like lymph, blood,flesh, bone-marrow, semen and body-waste (urine, fasces and sweat) and who has self control of sense organs and mind, such a person has been defined as a healthy person.

According to WHO(World Health Organisation):

Health in its broader sense can be defined as a state of complete physical, mental, and social well-being and not merely the absence of disease or infirmity.

That’s similar to the description in ancient texts. Don’t you think?


The healthy heart

Hriday is the hindi for heart which comes from the sanskrit word Hridayam.

Satapatha Brahmana of Yajur veda, defines Hridayam as:

  • Hru” meaning “harinay” or “that receives”
  • Da” meaning “daanay” or “that gives”
  • Ya” meaning “enngathaw” or “that circulates”

So, that which receives, gives and circulates blood is called Hridayam.

Sushruta says:

kapha pittavaruddhastu maruto rasa murcitah

hrdisthah kurute sulam uccvasarodhakam param

which means…

Heart diseases are caused because of “kapha” and “pita” defects and thus thickening and narrowing of coronary arteries resulting in acute pain in the chest and difficulty in breathing.

Woah! Indians knew that heart receives and circulates blood even before Christ descended!


Pythagoras theorem? Or was it someone else’s ?

dirgha caturasasyaksnya rajjuh parsvamani tiryak mani ca

yatprthagbhu te kurutah tadubhayam karoti

( Baudhyana sulba sutras ch 1–12 sloka)

In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Should have been Baudhyana’s theorem. Right?


What defines a ‘machine’?

dandaiscakraisca dantaisca sarani bhramanadibbhih

sakterutpadanam kim va calanam yantramucyate

(Yantra-varnavam)

Yantra or machine containing parts such as danda – lever, chakra – pulley, danta – toothed wheel, sarani – inclined plane and bhramana – screw; is used to produce or divert force.

Maybe, just maybe… there was an IIT in ancient India.


String theory is a modern development. Or is it?

mattah parataram nanyat kincidasti dhanajaya

mayi sarvamidam protam sutre manigana iva

(Bhagvad Gita 7.7)

Krishna says, “Like pearls strung in a string, the whole cosmos is strung in giants strings tethered to me”

And modern physicists say the same too, that string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. It describes how these strings propagate through space and interact with each other.


Solar and lunar eclipse.

chadayati sasi suryam sasinam mahati ca bhuchaya

(Aryabhattam, Golapada sloka 37)

When moon shadows the Sun, solar eclipse occurs. When earth shadows the moon, lunar eclipse occurs.

Again, ancient Indians! Phew!


Darwin’s theory of evolution. Or was it someone else’s ?

jatyantara parinama prakrtya purat

(Patanjali Yoga sutras 4.2)

Internal nature is the main reason for transformation from one species to another. This change is caused by the inflow of the organism’s behaviours due to the external environment.

Darwin? Plagiarism?


Generation of electricity.

samsthapya mrnmayam patram tamrapatram susamskrtam

cadayet sikhigrivena cardrabhih kasthapamsubhih

dastalosto nidhatatvah paradaccaditastatah

utpadayati tanmitram samyogastamradastayoh

(Agastya Samhita – Shilpa sastra sara)

Place a well-cleaned copper plate in an earthenware vessel. Cover it first by copper sulphate and then moist sawdust. After that put a mercury-amalgamated-zinc powder on top of it.

A chain of one hundred jars is said to give a very active and effective electromotive force.

When a cell was prepared according to Agastya Samhita, it was found to produce a potential difference of 1.138V.


Origin of Lenses.

aprapya grahanam kacabhra patala sphatikantarito palabdheh

(Nyaya darshana 3.46)

That which cannot be viewed by the naked eyes, can be viewed with the help of kacha – glass, abrapatala – mica and spatika – crystal.


Spherical Earth. We knew it first.

Bhugolah sarvato vrtah

(Aryabhattiyam, Golapada 6th sloka)

The Earth looks round from all sides.

Madhye samantandasya bhugolo vyomni tisthati

(Surya Siddhanta ch 12 sloka 32)

In the midst of the universe, the spherical earth stands firm in space.

The ancient Indians knew it well before Copernicus.


Check out this comment on the number system by Shubhangi Shree.


I think that would be enough.

So you see, the ancient Indian texts aren’t just poetry meant for entertainment.

They’re poetry meant for enlightenment… of the mind and soul.

🙂


EDIT (17 Jan 2017):

Since a number of people are messaging me for the source of these facts, I decided to put up the names of the books which I read to write this answer of mine.

They are as follows:

Why do many people today claim that ancient Indian texts contain advanced science?

What are some motivational pics that inspire you?

What are some motivational pics that inspire you? by Shivam Sundriyal

Answer by Shivam Sundriyal:

Don't get disappoint if you failed to be her husband.. But make sure you become her husband's boss

People will bring your past.. if they are scared by your present

If nobody hates you.. you are doing something boring

If you born poor, it's not your mistake.. but if you die poor, it's your mistake

What seems impossible today.. will one day become your warm-up

5AM.. The hour when legends are either waking up ,or going to sleep

Fall seven times.. and stand up eight

Just remember.. even your worst days have only 24 hours

Great things take time.. don't give up

My feelings for her won’t give my mom a great life.. my hard work and sacrifice will give

You can't give someone what you don't have. Build yourself first.. then build others

Sacrifice a few years of partying.. for the decades of freedom

Start by doing what's necessary. Then do what's possible.. and suddenly you are doing the impossible

Kill them with success.. and bury them with a smile

Excuses will turn your dreams into dust

Insanity is doing things over and over.. and expecting different results

Remember that someone thinks that you are the most amazing person they know

Thukra Diya jinhone mujhe mera waqt dekhkar.. kasam khata hoo aisa waqt launga ki milna padega mujhse waqt lekar

The fool didn’t know it was impossible.. so he did it

LIFE GOAL

What are some motivational pics that inspire you?

What is a rain check?

What is a rain check? by Stephanie Vardavas

Answer by Stephanie Vardavas:

Before the era of electronic ticketing, if you bought a ticket to a professional baseball game it was a small strip of card stock, perforated in a couple of places. When you presented your ticket for entrance to the ballpark, about half of it would be torn off by the ticket taker and you would keep the rest. It would be marked with your seat location and other necessary information, including a section labeled RAIN CHECK.

In the event rain canceled the game before enough innings were played for it to become a legal game, you could present your rain check at the box office for a ticket to another game.

This is a rain check.

In any other usage, “rain check” is a metaphor, signifying that you have the right to come back on another day to receive the thing you could not get today. In a store it means “we are sold out of the item you want, so here is a slip of paper entitling you to buy one at the same price when we get more of it in stock.” In a social setting it is strictly oral and means, “I have a conflict so I am not available for the social event to which you have invited me, but I hope that you will invite me again some other time.”

What is a rain check?

What is the scariest code you have ever seen?

What is the scariest code you have ever seen? by Ashok Agarwal

Answer by Ashok Agarwal:

To answer your question, I would pick Malbolge programming language.

Here’s the code for “Hello World!”

 (=<`#9]~6ZY32Vx/4Rs+0No-&Jk)"Fh}|Bcy?`=*z]Kw%oG4UUS0/@-ejc(:'8dc

Appears to be all special characters and gibberish, right? Here’s what Wikipedia says about this language:

“Malbolge is a public domain esoteric programming language invented by Ben Olmstead in 1998, named after the eighth circle of hell in Dante's Inferno, the Malebolge. Malbolge was specifically designed to be almost impossible to use, via a counter-intuitive 'crazy operation', base-three arithmetic, and self-altering code.

Malbolge was so difficult to understand when it arrived that it took two years for the first Malbolge program to appear. Indeed, the author himself has never written a single Malbolge program. The first program was not written by a human being: it was generated by a beam search algorithm designed by Andrew Cooke and implemented in Lisp.”

Here’s another example of Malbolge. It takes input from user (string) and prints it on screen.

(aBA@?>=<;:9876543210/.-,JH)('&%$#"!~}|{zy\J6utsrq
ponmlkjihgJ%dcba`_^]\[ZYXWVUTSRQPONMLKJIHGF('C%$$^
K~<;4987654321a/.-,\*)
j
!~%|{zya}|{zyxwvutsrqSonmlO
jLhg`edcba`_^]\[ZYXWV8TSRQ4
ONM/KJIBGFE>CBA@?>=<;{9876w
43210/.-m+*)('&%$#"!~}|{zy\
wvunslqponmlkjihgfedcEa`_^A
\>ZYXWPUTSRQPONMLKJIH*FEDC&
A@?>=<;:9876543210/.-m+*)(i
&%$#"!~}|{zyxwvutsrqpRnmlkN
ihgfedcba`_^]\[ZYXWVU7SRQP3
NMLKJIHGFEDCBA@?>=<;:z8765v
3210/.-,+*)('&%$#"!~}_{zyx[
vutsrqjonmlejihgfedcba`_^]@
[ZYXWVUTSRo

Malbolge is an esoteric programming language. An esoteric programming language (sometimes shortened to esolang) is a programming language designed to test the boundaries of computer programming language design, as a proof of concept, as software art, as a hacking interface to another language, or as a joke.

What is the scariest code you have ever seen?