Binaries Are Overrated

A blog about Drarry and mathematics. Tags will be used, so make good use of Tumblr Savior.

[twocubes]

All right! So:

I was commissioned to illustrate how a given everywhere-continuous but nowhere-differentiable function fails to be differentiable.

So I made this one up! It’s basically a sum of functions f at the top there.

Anyways you can see at the bottom how when you zoom in on the curve the slope of the secant doesn’t converge and so the function isn’t differentiable (on the right)

[mindfuckmath-deactivated2016062]

GIMPS has discovered a new Mersenne prime number: 2^74207281-1 is prime! Discovered: 2016 Jan 07

The 49th Mersenne prime (and the largest prime number to date) has been discovered!  

[dictacontrion]

Harry moped for weeks. Ron was completely bewildered by his abrupt change in mood, and made daily attempts to guess the reason behind it. “Did you and my sister get into a fight?” “Are you worried about the last year of training?” “You’re upset that I’ll be moving out next year, aren’t you?” “It has to be Ginny! She won’t tell me anything. What did she do?” “Is it the situation in the Middle East? It sucks, doesn’t it?” “Did someone say something mean about you in the papers? Do I need to have a talk with Rita?” By mid-August, Ron had gotten desperate. “Are you pregnant?” “What?!” said Harry, looking up from his cereal. “Is that even possible?” “I dunno. You hear stories.”

Welcome to the Broom Closet by incapricious (via dictacontrion)

[cosmicbeachparty]

A happy number is a number defined by the following process: Starting with any positive integer, replace the number by the sum of the squares of its digits, and repeat the process until the number equals 1 (where it will stay), or it loops endlessly in a cycle which does not include 1. Those numbers for which this process ends in 1 are happy numbers, while those that do not end in 1 are unhappy numbers (or sad numbers).

[realworldmath]

What the hell is knot theory?

Knot theory is one of those fields in mathematics that falls squarely into the camp of “totally random seemingly useless but actually really cool”. Borne out of the flawed theory that atoms are knotted vortices in the aether of space, what is now known formally as knot theory was first considered by the British Physicist Lord Kelvin in the late 1800s. By the time Kelvin’s physical model had been proven incorrect, interest in knot theory had already gained traction among some of Europe’s most innovative mathematicians. Since then, it’s developed into a full-fledged sub-field of mathematics, relating to other fields as diverse as topology, graph theory, physics, abstract algebra, and theoretical computer science.

There are 3 things that make a mathematician’s knot different than a regular knot: (1) A knot’s string is one continuous loop, with each end connected to other (think of fusing the ends of your shoelaces together). (2) A knot is infinitely stretchy, flexible, and malleable. And (3) you can NEVER cut a knot, even if you glue it back together.

The main problem of knot theory can be stated in very simple terms: When are two knots “different”? Or more specifically, given any two knots, is it possible to twist, contort, stretch or deform one of them (without cutting!) so that it looks like the other? If you’re like the dozens of people who I’ve explained knot theory to in the past, I know what you’re thinking: “Okay, that sounds kind of interesting. So what is it good for?”

Though knot theory started out as nothing more than the curious pursuit of a few mathematicians with too much time on their hands, you’ll be surprised to know it has found real world applications in non-mathematical fields. Among other applications, it has been used to study the formation of DNA molecules in biology and may play a part in the development of quantum computers.

Knot theory as a prime example of why it remains so important to study, develop, and explore new mathematics. What often starts out as an trivial game of the mind, turns out to have far reaching and unexpected applications.

Full Disclosure: I wrote a thesis on a topic in Virtual Knot Theory.

[mathprofessorquotes]

There’s a lot of things you can do in the dark. Mathematics is not one of them.

Math teacher after a power outage (via mathprofessorquotes)

[computersciencetumbld]

Euclid and the First Non-Trivial Algorithm

Euclid is this guy:

(source)

He is best known for the derivation of all geometric truths using an axiomatic system (referred to as Euclidian Geometry).

He is also credited with writing the first non-trivial algorithm. His algorithm solves the Greatest Common Divisor (GCD) problem*. There had been algorithms developed before Euclid’s algorithm for GCD, such as for adding two numbers, or multiplying two numbers, but Euclid’s stands out. Before going to much into the “non-trivial” part, lets look at the algorithm itself.

This function takes two numbers, a and b, and recursively** finds the greatest common divisor. At first glance, this function doesn’t exactly look like it would work, because it doesn’t look like it is doing much. But this algorithm harnesses the power of the modulo!

“Mod” is an arithmetic operator that takes two operands. You can think of it like division, except instead of keeping the number of times that a goes into b, you keep the remainder. So 8%3=2 and 8%2=0. If a%b returns 0, then b is a divisor of a. So when b == 0, we have found the largest number that divides both a and b.

This is why Euclid’s GCD algorithm is considered the first non-trivial algorithm. It uses recursion, seems to require a formal proof in order to be proven, and can indeed be proven to be correct for any two positive integers.

*GCD problem = the problem of finding the largest number that divides two positive integers

**recursion = when a function calls itself (more here)

[the-perks-of-being-black]

“Eritrean-American Haben Girma, who is the first deaf-blind graduate at Harvard Law School’s story is a true inspiration.

Girma’s extraordinary story highlights her courage and determination despite physical challenges, and she is living proof that disability is certainly no barrier to achieving academic excellence.

Girma is an attorney who ‘advocates for the civil rights of persons with disabilities. A celebrated speaker, she provided the introductory remarks for the 25th Anniversary of the ADA [Americans with Disabilities Act] at the White House’.

…Girma appreciates the opportunities she has been offered and ‘the hard won power of the ADA.’” by Arthur Chatora, This is Africa

“Haben Girma is our new hero. The 27-year-old lawyer is the first deaf-blind alumna of Harvard Law School.

After graduating magna cum laude with an undergraduate degree from Lewis & Clark College in 2010, Girma went on to earn her Juris Doctor (JD) degree from Harvard in 2013.

…Haben, who was also on Harvard’s Ballroom Dance Team, is originally from the East African country of Eritrea. Her older brother was also born deaf-blind, and the pair was told their disabilities were ‘…a curse on the family.’

…The budding activist and civil rights attorney currently works for the Disability Rights Advocates law firm in Sacramento helping others fight for their rights under the ADA.

Haben said that her grandmother, who still lives in Eritrea, believes her success is ‘like magic.’ She closed her speech by saying, ‘…People with disabilities succeed not by magic, but from the opportunities afforded by America and the hard-won power of the ADA.’

President Obama then said, ‘Thank you Haben for making sure students with disabilities have access to a world class education just as you have.’ Zon D'Amour, HelloBeautiful/Global Grind

“By the time Girma was born in 1988, six years younger than her brother, her mother had made a refugee’s journey from Eritrea to the United States. And in California, a deaf-blind girl like Girma had a legal right to an education.

In public schools in Oakland, she was educated alongside other students, leaving her mainstream classes for an hour a day to learn Braille.

…In the winter of 1983, Girma’s mother, Saba Gebreyesus, left Eritrea. The war of independence with Ethiopia was going on. It was a two-week trek to Sudan, ‘walking at night to try to avoid the different military groups fighting in that area.’ At one point she slept in a tree surrounded by hungry hyenas.

A Catholic resettlement agency helped Gebreyesus move to the United States.

In the United States, disability civil rights laws provided opportunities to Girma. TheIDEA law says every child with a disability is guaranteed an education, and the ADA bans discrimination based on disability.

…At the White House, Girma talked to the president one on one, telling him ‘that technology can bridge the gap for people with disabilities.’ The president typed on a silver, wireless keyboard, and Girma read the message on a digital Braille device (the technology that enabled us to conduct our phone interview with her). The back-and-forth was instantaneous….

…Today, her brother, Mussie Gebre, travels around California, teaching people with disabilities how to use technology — like the devices that help him and his sister.

‘To all of us here,’ Girma said to the crowd in the East Room at the White House, ‘we know that people with disabilities succeed not by magic but from the opportunities afforded by America and the hard-won power of the ADA.’” by Joseph Shapiro, NPR

[dreadpiratemary-deactivated2018]

Today I made people cry.

I feel a little bit bad, except for the fact that I teared up when I wrote it. There’s also an evil, dark part of my that thinks I should buy stock in Kleenex and write more sad stories.

More tears = more dividends

[thetrichotomy]

I love that evil, dark part of you a lot more than I should, probably :P

[did-you-know]

William was fascinated by science. One day, he opened a textbook and saw a picture of a windmill, and his life changed forever.

“I was very interested when I saw the windmill could make electricity and pump water. I thought: ‘That could be a defence against hunger. Maybe I should build one for myself’.”

Neighbors found it very strange that he was spending so much time sifting through garbage. “Many, including my mother, thought I was going crazy. They had never seen a windmill before.”

“People thought I was smoking marijuana. So I told them I was only making something for juju [magic].’ Then they said: ‘Ah, I see.’”

He built a 16-ft-tall turbine from spare bicycle parts, a tractor fan blade, and an old shock absorber, and made blades out of plastic pipes- amazing the entire village when he climbed to the top and plugged in a light bulb that slowly flickered to life.

A book titled ‘The Boy Who Harnessed the Wind’ was written about his story, as well as a documentary called ‘William and the Windmill.’

Source

[curiosamathematica]

‘Outsiders’ Crack a 50-Year-Old Math Problem

Three computer scientists have solved a problem central to a dozen far-flung mathematical fields.

In 2008, Daniel Spielman told his Yale University colleague Gil Kalai about a computer science problem he was working on, concerning how to “sparsify” a network so that it has fewer connections between nodes but still preserves the essential features of the original network.

Network sparsification has applications in data compression and efficient computation, but Spielman’s particular problem suggested something different to Kalai. It seemed connected to the famous Kadison-Singer problem, a question about the foundations of quantum physics that had remained unsolved for almost 50 years.

The problem was solved in 2013.

[scientificphilosopher]

I followed a golden rule, whenever a new observation or thought came across me, which was opposed to my general results, to make a memorandum of it without fail and at once; for I had found by experience that such facts and thoughts were far more apt to escape from the memory than favorable ones.

Charles Darwin (via scientificphilosopher)

[hurricane-euler]

*nervous laughter*

[lthmath]

[allofthemath]

[theenglishcrux]

Mathematics

Mathematics - “eager to learn”

“Because the early Greek thinkers saw numbers as a ay to help them explain relationships, they spent much time developing formulas and equations. As a reslt, the Greeks used their adjective mathematikos, meaning “eager to learn” for the new science.” - In a Word by Rosalie Baker

Img//Word

[lthmath]

By: https://xkcd.com/872/

On 12 January we celebrated the birthday of a French author Charles Perrault (born on 12 January 1628). He laid the foundations for a new literary genre, the fairy tale, so I thought that this image would work perfectly with the day ^_^