#cyclotomic

[mathhombre]

Cyclotomic Roots

Mathober Day 21: Cyclotomic

Either new to me or forgotten, I loved digging into this idea. The nth cyclotomic polynomial is the largest degree factor of x^n-1 which divides no x^m-1 for m<n. You have to put it that way, because if a prime p divides n, then the pth cyclotomic divides x^n-1. Anyhow, the result of this is that the roots of the nth cyclotomic correlate to the fractions i/n that are irreducible.

So for x^15-1, we get 1/15, 2/15, 4/15, 7/15, 8/15, 11/15, 13/15, 14/15 as the roots of unity of the 15th cyclotomic, x^8-x^7+x^5-x^4+x^3-x+1. You can find them by dividing by the prime factors cyclotomics, which all have the form x^(p-1)+x^(p-2)+...+x^2+x+1.

Just beautiful! I added the sectors to make it prettier to see. Not sorry.

I couldn't get GGB to multiply out the roots of unity to get the polynomials, but that would be pretty cool. Play with it as is, though, here.

Oh, ok. One more: 99

[vodkablossoms-blog]

@psychlotomic replied to your post “Can u believe I DMed all of 5sos telling them it was my birthday and...”

did u send ur address

yep and emergency phone number just in case !!

[vodkablossoms-blog]

@psychlotomic replied to your photoset “

idk about u but I’m feelin’ 22”

hap hap hap birthday angel <3

thank you nina!! xx

[cbaekmx]

psychlotomic replied to your post “im a disaster i spilled a load of sugar on my bed and then i cried for...”

sienna i think you're the sweetest <333 big love

you’re the best nina truly :”)

[gloryhollanovjah]

IN CASE ANYONE WAS WONDERING

THIS is the best tag I have

[cyclogenesis]

I'm so glad you like the idea. If i was as good at writing as you and nina i would definitely do it, but how i am not, if you do it you would make me so damn happy because it is constantly in my head and i love the song so much. So yeah I'm so happy you liked it, have a good day sara :D

Aw please!! I'm still thinking about it a lot, something might come of it. :x You have a good day too honeybun <3

[cbaekmx]

Once you get this you have to say five things you like about yourself, publicly, then send it to 10 of your favourite followers ^-^

oh gee alrighty lets get down to business 

1. my taste in people is absolutely fantastic, my friends are my favourite people in the whole entire world!!

2. love my eyelashes they’re really nice thanks dad

3. i like that it’s easy for me to understand where a person is coming from even if i dont agree to it???? idk i’m like open and i can understand why a person says a thing??? IDK what im trying to say but anyways

4. my freckles omg i love them they’re so good, especially the ones on my arms they’re so nice

5. im a great big sister, im so great with children!!! i love them and i want 43

[oldusername]

Nina cyclotomic tagged me! (Thank you so much?! Ily!)

2. Last phone call= My dad as he's in Aberdeen and I haven't seen him in an age :(

3. Last text message= “I'm here and you are not!!!" (to my friend when she'd arranged to meet me and was running late) 4. Last song you listened to= I think it was black eyed by placebo or an old panic at the disco song on an 8tracks mix! 5. Last time you cried= This morning when I was tossing and turning and couldn't sleep and I knew i had school soon but they were tears of frustration

HAVE YOU EVER: 6. Dated someone twice= Nope! 7. Been cheated on= Yeah I'm pretty sure 8. Kissed someone and regretted it= yes 9. Lost someone special= Not really 10. Been depressed= Nope, I've certainly been through sad bouts though 11. Been drunk and threw up= Never been drunk to the extent of throwing up 

LIST THREE FAVOURITE COLOURS: 1. White 2. Grey 3. Light Blue

IN THE LAST YEAR, HAVE YOU: 15. Made a new friend= Yeah! 16. Fallen out of love= No but I've been through a break up 17. Laughed until you cried= Yes definitely, I was pretty close to it today in fact! 18. Met someone who changed you= Yes 19. Found out who your true friends are= 1000000000% yes 20. Found out someone was talking about you= Yep! 21. Kissed anyone on your FB friend’s list= Nope

GENERAL: 22. How many people on your FB friends list do you know in real life=  Almost all but I know everyone on my friends list and speak to them often 24. Do you have any pets= Two kitty cats and a dog :) 25. Do you want to change your name= Nope I like my name 26. What did you do for your last birthday= Went out for lunch with friends then spent the evening with various family it was a lovely day 27. What time did you wake up today= Ughhh I didn't really manage to get to sleep I was drifting in and out but I got out of bed at 4:30am :( 28. What were you doing at midnight last night= Watching the Great British Bake Off tips smh 29. Name something you CANNOT wait for= My holiday next month and my awful exams to be over and London with my friends and my 5sos gig! 30. Last time you saw your mother= Yesterday 31. What is the one thing you wish you could change about your life= For time to fast forward about 3 months or my classes not to be so very stressful 

32. What are you listening to right now= Nothing! 33. Have you ever talked to a person named Tom?= Yeah 34. What’s getting on your nerves right now= How tired I am when it's only 6:30pm 35. Most visited webpage= Tumblr or Youtube most likely 36. Blood type= O Negative I think? 37. Nickname= Reeb smh 38. Relationship status= Very single 39. Zodiac sign= Scorpio 40. Pronouns= She/her/hers 41. Elementary= ?? Just a public primary school 42. High School= Poorly funded high school with very good teachers 43. College= Not been yet, my goal is to go straight to University  to minimize the time I have to spend in higher education tbh but that all depends on my exam results, if I do go to Uni any time soon it would most likely be in Edinburgh 44. Hair colour= Dark Brown 45. Long or short= Mine is so short and I'm painstakingly growing it 46. Height= 5’6 47. Do you have a crush on someone?= Not at the moment but I fall in love with every cute girl on the street so 48. What do you like about yourself?= Eyes and lips and boobs!  50. Tattoos= None and no idea what I'm fond enough of to get on me forever right now  51. Righty or lefty= Righty 52. First surgery= My nose because I had breathing problems, first and only surgery  53. First piercing= Ears 54. First best friend= A girl who used to hang around my dad's neighbours house 55. First sport you joined= Netball 56. First vacation= Probably a caravan holiday or something but I've been on quite a lot more interesting ones 58. First pair of trainers= Who seriously knows this?

RIGHT NOW: 59. Eating= Nothing 60. Drinking= Water

61. I’m about to= Snuggle up with my cat who's nagging at me and go to sleep!

62. Listening to= Nothing

63. Waiting for= My phone to charge up so I can set my alarm 64. Want kids?= YES so many!! 65. Get married?= Definitely  66. Career?= Journalist or something in political science (snore)

WHICH IS BETTER: 67. Lips or eyes= Oh no um eyes 68. Hugs or kisses= I love both 69. Shorter or taller= Taller 70. Older or younger= Older 71. Romantic or spontaneous= Spontaneous 72. Nice stomach or nice arms= Tums :) 73. Sensitive or loud= Sensitive 74. Hook-up or relationship= Relationship 75. Trouble maker or hesitant= Hesitant

HAVE YOU EVER: 76. Kissed a stranger= Nope 77. Drank hard liquor= Yes and I was far too young to have done so! 78. Lost glasses/contacts= Nope don't wear them 79. Sex on first date= Noo 80. Broke someone’s heart= I think so but it was 100% their fault! 81. Had your own heart broken= Yeah 82. Been arrested= Nope 83. Turned someone down= Yes and felt awful ahh 84. Cried when someone died= No 85. Fallen for a friend= Let's not get into that

DO YOU BELIEVE IN: 86. Yourself= Yes a whole lot 87. Miracles= Nope 88. Love at first sight= Yes 89. Heaven= No 90. Santa Claus= No 91. Kiss on the first date= Yeah nothing wrong with that! 92. Angels= Nope

Thank you so much Nina you're a star this was quite fun! I tag hillsinthesheets buildingmatchstickhouses and femkinkmichael