#integers

[positivelyprime]

Eisenstein primes (and integers)

You've heard of integer primes, but have you heard of different kind of primes? One of the most beautiful pictures in mathematics I've recently seen is this:

This is a picture displaying the Eisenstein primes and the rest of the post will be me explaining where this comes from.

Firstly, to understand what Eisenstein primes are, we need to know what Eisenstein integers are! An Eisenstein integer is a complex number of the form z = a + b w where a,b are integers and w = e^(2/3 pi i). Normally a small letter omega is used instead of w. Notice that w is a third root of unity, i.e. w³ = 1.

Appending this complex w to the regular integers has some consequences. In particular, we can now view the eligible numbers on the complex plane to get this picture:

The Eisenstein integers correspond exactly to places where two dotted lines cross. As such, where normally one can view integers as laying on a 1-d line, we can now view Eisenstein integers as laying on a 2-d lattice!

Now one may start to wonder if, just like in the integers, one can have Eisenstein integers which are not divisible by other Eisenstein integers. In more mathematics: We call a number p an Eisenstein prime if p cannot be written as a*b where a,b are Eisenstein numbers which are not +-1, +-w, +-w² (the units in this system).

It turns out that some regular primes are still primes in the Eisenstein integers. For example, 2 can still not be decomposed. However, 3 can! We may write 3 = -(1+2w)(1+2w) which means that 3 is not an Eisenstein prime. One may investigate this further (using abstract algebra) to arrive at the picture at the top of this post. The 6-fold rotational symmetry is due to the Eisenstein integers having 6 units.

Of course a natural question is why take a third root of unity and not an nth root? This is a very interesting question and leads to the study of (integer rings of) cyclotomic fields! This concludes fun math fact tuesday

#math #mathblr #mathematics #prime numbers #primes #integers #maths #fun math fact tuesday

[secondwheel]

The  |  stands for the absolute value of an integer. In this case, it makes anything positive. 

#maths #math #integrals #calculus #integers #school #studying #studyblr #memes #meme #student memes #reddit memes #funny #relatable #humour #humor #science #insidesjoke

[xxyv3]

quick pi doodle, i forgkt to put my signatur on my last art

#object #object oc #object shows #objectshow #objectsona #osc #tpot #tpot fanart #bfdi #bfdia #pi #symbolar #Integers

[sleekwind]

What I don't understand is when math teacher says -1 is the largest negative integer. What about -0.1? Or -0.000534? Are they not right side enough in the integer scale for them to be large? If there is a math side of Tumblr pls explain

#integers #numbers #maths #math struggles

[zwoelffarben]

#poll #math #integer #integers

[planeswalker-umbral]

Oh you think healers can't get kills?

*heals you 2147483648 health*

#video games #healers #support #integers #overflow #32 bit #coding #rpg #uploads #cleric

[noelements-setempty]

Integers like their personal space. Real numbers are clingy huggers. Rational numbers look like they're super touchy-feely but they're actually just standing really close together.

#integers #real numbers #rational numbers #silly maths thoughts #silly math thoughts

[brightgreendandelions]

by "how many digits" i, of course, mean log base ten! that's why 0 and 1 are separate options :)

#textpost #math #numbers #integers #favorite number #poll #polls

[mumblelard]

the shirt for my new hiking club has finally arrived

#hikikomori #hermits #ramblers #entrails #interiors #integers #the plane has crashed into the god damn mountain #one day i'm sure we'll get together #how i rose from the dead in my spare time and you can too #this monkeys gone to heaven

[lesbianslovebts]

I was thinking about partitions of integers and playing around with Ferrers diagrams for 1 through 7 tonight. So, I drew them all out vertically and paired the symmetrical shapes (see the margins of the page). Then, I redrew them so the symmetry was more easily visible (middle of the page). I moved them around some more so that there weren't any spaces between each partition diagram and nested them all together like matryoshka dolls (bottom right). I thought that looked cool but wanted to get rid of the extra space, so I pushed it all together. Lastly, I figured I would reflect the whole thing across y = x to get a nice square. The final design is the second photo!

#mathematics #math #mathblr #integers #partitions #ferrers shapes #ferrers diagrams #number theory #math art #llbtsart #llbtspost

[thesilliestgeese]

the sexual tension between relatively prime numbers is unbearable

#integers

[legoobsessionist]

Courtesy of my new year's party: every integer 1-104 ranked by sexiness

#take 5 #tierlist #numbers #integers

[digitalartform]

#integers #8bit #16bit #displacement map

[dharmendrajadav0208]

integers || Introduction | definition of integers

Std 7 maths chap 1 integers

For primary students

#youtube #education #maths #maths problem #Maths Rules #Integers #Std7maths #Youtubevideo #Ytshorts #Shortsfeed #Trending #Mathshorts #artists on tumblr

[my-experience-2023]

Learning integers, natural and expressive

One of the most important topics in mathematics during education is integers, natural and expressive numbers. Although this subject in mathematics is very important, it seems that students have a little difficulty in learning this subject. In order for students to be able to learn the subject of integers, natural and rational numbers well, it is necessary to adopt the correct teaching method. If you visit the site address that we put on this page, you will find out everything you need to know about learning this topic.

#integers #natural and expressive numbers

[mathswithnarendrasir]

Class-9 CBSE -NCERT Solution Polynomials | Q4 #mathematics #narendrasir

#No views 20 Feb 2023 #In this video you will learn about classification of real numbers such as rational #irrational #integers #whole and natural numbers. #Also in the end you will learn how to find rational numbers between two rational numbers. #Previous Video: #✔️📚👉 Watch Full free Course:- https://aaetclasses.in/our-courses/ #✔️📚👉 Get Notes Here: https://aaetclasses.in/free-notes/ #✔️📚👉 Get All Subjects playlists:- #✔️ Class: 9th #✔️ Subject: Math’s #✔️ Chapter: Rational Numbers (Chapter 1) #✔️ Topic Name: Rational Numbers - Introduction/ Concepts & Examples #✔️ Topics Covered in This Video: Properties of Rational Numbers: Closure #Commutativity #Associative #Distributivity #Examples of Rational Numbers #======================================================= #Why study from Math’s with Narendra Sir? #Math’s with Narendra Sir is an online education platform that helps gives You NCERT/CBSE curriculum based free full courses that you can pe #👉 Contact us #➡️ Connect with us: [phone] #➡️ Website: https://aaetclasses.in/ #➡️ Subscribe to us on YouTube: - https://www.youtube.com/@mathswithnar... #➡️ Facebook: https://www.facebook.com/profile.php?... #➡️ Instagram: #➡️ Telegram: https://t.me/mathswithnk #➡️ koo: https://www.kooapp.com/feed