Countdown to 2020:
It seems that every New Year’s Eve, mathematicians come up with equations with the new year in it. Some of those equations will be a countdown. Here is the equation that I found and made into a gif:
Factors of 2020:
- 2020 is a composite number.
- Prime factorization: 2020 = 2 × 2 × 5 × 101, which can be written 2020 = 2² × 5 × 101
- 2020 has at least one exponent greater than 1 in its prime factorization so √2020 can be simplified. Taking the factor pair from the factor pair table below with the largest square number factor, we get √2020 = (√4)(√505) = 2√505
- The exponents in the prime factorization are 2, 1, and 1. Adding one to each exponent and multiplying we get (2 + 1)(1 + 1)(1 + 1) = 3 × 2 × 2 = 12. Therefore 2020 has exactly 12 factors.
- The factors of 2020 are outlined with their factor pair partners in the graphic below.
A 2020 Factor Tree and a 2020 Factor Cake:
Or a 2020 Factor Cake:
Other Facts about the number 2020:
2020 is palindrome 4C4 in BASE 21 (C is 12 in base 10):
4(21²) + 12(21) + 4(1) = 4(441) + 12(21) + 4 = 1764 + 252 + 4 = 2020
42² + 16² = 2020
38² + 24² = 2020
2020 is the hypotenuse of FOUR Pythagorean triples:
400-1980-2020 which is 20 times (20-99-101)
868-1824-2020 calculated from 38² – 24², 2(38)(24), 38² + 24²
1212-1616-2020 which is (3-4-5) times 404
1344-1508-2020 calculated from 2(42)(16), 42² – 16², 42² + 16²
2020 is the difference of two squares two different ways:
506² – 504² = 2020
106² – 96² = 2020
Can you calculate when 2020 is a leg in a Pythagorean triple from those equations? (The Pythagorean triples can be calculated from a² – b², 2(a)(b), a² + b²)
Then can you calculate other times 2020 is a leg in a Pythagorean triple from these facts? (The Pythagorean triples can be calculated from 2(a)(b), a² – b², a² + b²)
2(1010)(1) = 2020
2(505)(2) = 2020
2(202)(5) = 2020
2(101)(10) = 2020
Did any of those equations produce the same Pythagorean triples that the difference of two squares produced?
2020 is the sum of four squares in MANY different ways. Here is how I found two of those ways:
Twitter Posts I’ve Seen about the Number 2020:
2020 is an autobiographical number, because in the base of the number of its digits (4) it describes itself: It has 2 zeroes, 0 ones, 2 twos and 0 threes. The largest and only decimal autobiographical number is 6,210,001,000 • https://t.co/fOBeHMzi4u #maths #math #HappyNewYear pic.twitter.com/QMfAzMgqku
— Maths Ed (@MathsEdIdeas) December 27, 2019
=(4)(5){4(25)+1}
=20 (100+1)
=20(101)
= 2020— Ziyanda Soya👜👠❤🗡🥊➕️ (@LadyZee50165267) December 27, 2019
— Karen Gholam Tabbal (@karengholam) December 28, 2019
2020 is the smallest number that can be written as the sum of the squares of four consecutive primes and as the sum of two squares in two ways #HappyNewYear #HappyNewYear2020 #maths #math
2020 = 17²+19²+23²+29²
2020 = 16²+42²
2020 = 24²+38²— Maths Ed (@MathsEdIdeas) December 29, 2019
مجموع مربعات 4 أعداد أولية متتالية 2020
17²+19²+23²+29²
عام 2020 سعيد pic.twitter.com/9AQ89cTt4k— الخوارزمي الصغير (@bergasmath) December 29, 2019
Day 364: #mathiratti pic.twitter.com/3uxeDS6PFK
— Diego Rattaggi 🇨🇭 (@diegorattaggi) December 30, 2019
Let’s Make a Factor Cake for 2020 https://t.co/NNlSeGW4hZ pic.twitter.com/GnVZy2o0fN
— Iva Sallay (@findthefactors) December 30, 2019
Math up your countdown to 2020… #HappyNewYear #HappyNewYear2020 #maths #math pic.twitter.com/wLnxBBZiVo
— Maths Ed (@MathsEdIdeas) December 30, 2019
It’s official: 10 x 9 x 8 + (7 + 6) x 5 x 4 x (3 + 2) x 1 = 2020 is this NYE’s most elegant countdown equation.https://t.co/I575FHKNJ6
— Alex Bellos (@alexbellos) December 30, 2019
So I looked up the official decade start.
There isn’t one. Math heads will say there was no year zero, so it starts Jan 1 2021. Sentimental people will say it starts Jan 1 2020.
By definition a decade can start any year, depending on what year one begins to measure.
So go ahead— BKinD (@BKinDetroit) December 30, 2019
Does your New Year Resolution List for 2020 look anything like this?
If so, send me a wee email (aap03102@gmail.com) and I might (!) be able to help….#MathsNewsletter#AlsoContainsTheMilkRota pic.twitter.com/YZnObCcbBI
— Chris Smith (@aap03102) December 30, 2019
At 20 seconds past 20:20 on this New Year’s Eve, we will be exactly 20 days away from it being 20 seconds past 20:20 on the 20th day of the year 2020 #Day202020 #HappyNewYear #HappyNewYear2020 pic.twitter.com/8XEqzdQOoF
— Maths Ed (@MathsEdIdeas) December 31, 2019
12 hours left on this one 🙂 https://t.co/wzviR7rsjz
— M Shah (@shahlock) December 31, 2019
Celebrate the year 2020. What can we say about 2020? Here are the divisors of 2020. pic.twitter.com/GaTSbsYhZR
— Cliff Pickover (@pickover) December 30, 2019
2020 =(ddddd −d)/dd × (d+d)/d
d∈(1,2,3,4,5,6,7,8,9)
— . (@Expert_Says) December 31, 2019
2020=(123+4)×(5+6)+7×89
2020=98+7+65+43^2+1.
— . (@Expert_Says) December 31, 2019
2020
＝16²+42²
＝24²+38²
＝18²+20²+36²
＝17²+19²+23²+29²
(連続する4つの素数の平方和)— ブリッジ@京大院 YouTubeで問題解説&教育情報 (@BridgeKyotouniv) December 30, 2019
2020=17²+19²+23²+29²#HappyNewYear2020 🎇#MathGIF w/ @geogebra pic.twitter.com/8wfOhfaErA
— Vincent Pantal🍩ni (@panlepan) December 31, 2019
Every day is a good day for Maths, but here’s a calendar I drew up of some extra fun Maths dates for 2020 🥳
Can’t wait for Pythagorean Triple Day 📐
What other cool dates have I missed? pic.twitter.com/snGb2McLGF
— Ayliean (@Ayliean) December 31, 2019
Wishing you a wonderful 2020🎉:
2020 = 402+403+404+405+406
2020 = 249+250+…+255+256
2020 = 31+32+33+…+70
2020 = 24² + 38²
2020 = 16² + 42²
2020 = 4² + 6² + 8² +…+ 22²
2020 = t₃ + t₄ + t₅ + … + t₂₂
(△ numbers)#happynewyear2020 pic.twitter.com/CMPOrwJfjm— Ed Southall (@solvemymaths) December 31, 2019
Happy New Year! Here’s some 2020 math. Start the countdown! #happynewyear2020
10*(9+8*7*6-5!-4!+3-2*1) = 2020
(10*9+8!/(7*6)-5*4!/3)*2*1 = 2020
10*(9+8)*7+6!+5!-4*3+2*1 = 2020
(10+9)*(8+7+6)*5+4!+3-2*1 = 2020
(10-9*8+7-6+5+4^(3!))/2*1 = 2020
10*(9+8*7-6+5!+4!)-3^2-1 = 2020
— Derek (the Halls) Orr (@Derektionary) December 31, 2019
How many ways can you get 2020 using 10 9 8 7 6 5 4 3 2 1 in that order?
— Ed Southall (@solvemymaths) December 31, 2019
🇪🇸¡Feliz año nuevo x a todos!🇬🇧 Happy New Year x to everyone!
x = 10 × 9 × 8 + 7 + 6 × 5 × 43 + 2 + 1— Ignacio Larrosa Cañestro (@ilarrosac) December 31, 2019
Una descomposición atractiva para 2020: los cubos de los cinco primeros números pares acompañados de los cuadrados correspondientes:
2020=2^3+2^2+4^3+4^2+6^3+6^2+8^3+8^2+10^3+10^2
— Antonio Roldán (@Connumeros) December 31, 2019
Here’s a special countdown for 2020. Happy New Year! pic.twitter.com/mxjD0evMDJ
— Fermat’s Library (@fermatslibrary) December 31, 2019
¡Feliz 2020!
En este año autobiográfico, escribid vuestra propia biografía, y no dejéis que los demás lo hagan por vosotros.
¡Feliz año nuevo!#AnoNuevo2020 #felizNochevieja #Feliz2020 #FelizAnoNuevo pic.twitter.com/YoWujsXtQs— MatematicasCercanas (@matescercanas) December 31, 2019
— matematik (@il1123) December 31, 2019
2020 is the hypotenuse of four Pythagorean triple triangles: 400-1980-2020 which is 20 times (20-99-101)
868-1824-2020 calculated from 38² – 24², 2(38)(24), 38² + 24²
1212-1616-2020 which is (3-4-5) times 404
1344-1508-2020 calculated from 2(42)(16), 42² – 16², 42² + 16² pic.twitter.com/4PJ2togatt— Iva Sallay (@findthefactors) December 31, 2019
Shiver in ecstasy. The year “2020” can be created using only the 9 digit. https://t.co/FHtffsaSFP pic.twitter.com/4SKrACQps0
— Cliff Pickover (@pickover) December 31, 2019
— Mrityunjoy Hazra (@3Mrityunjoy) December 31, 2019
#mathematics #mathteacher #teachmath #happynewyear2020
Answer(with surprise End): https://t.co/Aai4pg9moG pic.twitter.com/koLGfih57B
— Matematik_Man (@matematik_man) December 31, 2019
no primes or semi-primes for a whole year since every date will be divisible by 2x2x5 :/// https://t.co/WRf0U77FRx
— .json derulohoho 🎄 (@bathwater4jess) December 31, 2019
Happy New Year to all you educators who care about ‘ the kids’. #MTBoS #iteachmath #mathchat pic.twitter.com/JQdi4rcsi6
— Don Fraser (@DonFraser9) December 31, 2019
今年見つけた数式の、僕が好きなやつたちです pic.twitter.com/8lFGw1kfir
— 湧水(ゆうすい) (@Fujino_Yuusui) December 31, 2019
¡¡Feliz 2020!! pic.twitter.com/0fWPfIvUVS
— M. Ángeles Gil (@magilbla) December 31, 2019
I 💖 the 2020 GIF @solvemymaths made. The big finish is that 2020 is the sum of triangular numbers 😮. Good reminder. The sum of consecutive triangular numbers is a square 🟪. #iteachmath #HappyNewYear everybody. pic.twitter.com/DaVvLKv71u
— Jim Olsen (@DrOlsen314) December 31, 2019
2020 = [22 × 2 + (2⁰ ÷ (2⁰ + (2⁰ ÷ (2 × 2 × 2 × 2 + (2⁰ ÷ (2⁰ + (2⁰ ÷ (22 × 2 × 2 + (2⁰ ÷ (2⁰ + (2⁰ ÷ (2 × 2 × 2 × 2 + (2⁰ ÷ (2⁰ + (2⁰ ÷ (22 × 2 × 2 + (2⁰ ÷ … ]² #HappyNewYear #HappyNewYear2020 #maths #math pic.twitter.com/EF0w4LEM6G
— Maths Ed (@MathsEdIdeas) December 31, 2019
Finding 2020 in different bases. Which one doesn’t belong? pic.twitter.com/BDnDDbdKi1
— Iva Sallay (@findthefactors) December 31, 2019
Happy New Year! 🎆 pic.twitter.com/GwNMdwJf6y
— Ordinaryüs ∲ (@Caner_KMZ) December 31, 2019
Happy New Year 2²×5×101 🎆🎇🥂🎉 pic.twitter.com/5BYnk6ptX9
— Mathigon (@MathigonOrg) December 31, 2019
2020 es la suma de los cuadrados de cuatro números primos consecutivos: pic.twitter.com/9ZRQS0Pr3y
— fun with functions (@funfunfunctions) December 31, 2019
Veo publicados en las últimas horas muchos descensos de cifras para el 2020, así que me ha entrado el deseo de volver a compartir mi ascenso-descenso:
2020=(12+3+4)×(5!+6+7+8)-9-8×76-5-4-32-1
— Antonio Roldán (@Connumeros) December 31, 2019
Happy New Year. The year “2020” can be written like this, in binary. (Orange = 1; cyan = 0) pic.twitter.com/gashhAXLAz
— Cliff Pickover (@pickover) December 31, 2019
会員の皆さん。
今年も大変お世話になりました。
来年もどうぞ宜しくお願いします🤲好きな演算を用いて等式を完成させてください🎍 pic.twitter.com/Mis80KBwol
— 数学を愛する会 (@mathlava) December 31, 2019
Here’s a start 👍 https://t.co/elNqy1W7mj
— Ed Southall (@solvemymaths) December 31, 2019
This short work by Inder J. Taneja brings representations of 2020 in different situations. This is a special countdown for 2020. Happy New Year! [full paper: https://t.co/KhDmoEb7Sw] pic.twitter.com/FZncYrqc5K
— Massimo (@Rainmaker1973) December 31, 2019
Tras un año de emociones intensas, ojalá lo despidamos como es debido y recibamos un nuevo año cargado de salud e ilusiones nuevas. Se os quiere 😍 pic.twitter.com/O5m5OczNfc
— Julio Mulero (@juliomulero) December 31, 2019
Happy new year for all with @geogebra https://t.co/ZvlTKUzkOz#geogebra #MTBoS #ITeachMath #math #maths #EdTech #geometry #MathEd #FigureThat @mathieublossier
@bancoche @PerHenrikChris1 pic.twitter.com/ybUDQCMNBu— Daniel Mentrard (@dment37) December 31, 2019
@Mathematical_A @tweetprofmatt @nick_battle_uk
This is nice – it’s got the numbers from 1 to 10 involved – and in order too!
(And because everything is commutative, it works in ascending order as well.) https://t.co/8WHpycshGP— Mark Dawes (@mdawesmdawes) December 31, 2019
Una descomposición atractiva para 2020: los cubos de los cinco primeros números pares acompañados de los cuadrados correspondientes:
2020=2^3+2^2+4^3+4^2+6^3+6^2+8^3+8^2+10^3+10^2
— Antonio Roldán (@Connumeros) December 31, 2019
2020 con solo cinco factoriales:
2020=3!×8!/5!+2!+2!
— Antonio Roldán (@Connumeros) December 31, 2019
También vuelvo a compartir un ascenso del 1 al 9 para el nuevo año:
2020=(1+234+56)×7-8-9
— Antonio Roldán (@Connumeros) December 31, 2019
A todos mis amigos de Twitter, amantes de las matemáticas, les deseo un próspero, fructífero y feliz año nuevo: pic.twitter.com/nnX8Bgn64o
— Ignacio Mantilla Prada (@MantillaIgnacio) December 31, 2019
Una felicitación demostrada Pitagórica de @AMRamosDelOlmo para el 2020.#ChristMaths https://t.co/Ow9f07i52O
— Juan Miguel Ribera (@juanripu) December 31, 2019
Feliz 2020 #QueseadeHuelva pic.twitter.com/SYgozKWEtO
— Luis M. Iglesias (@luismiglesias) January 1, 2020
Happy New Year!
The 2020th decimal place of 𝛑 is 3.
The 2020th decimal place of ℯ is 3.
The 2020th decimal place of φ is 3.All three of these constants are believed to be ’normal’. How often do you expect their digits to coincide like this?
— Math In The News (@MathInTheNews) January 1, 2020
That’s how I count it: the 1st year of a decade ends in 1. But other more impatient folk consider we’re there already. We had the same problem with 1999 & 2000. Folk found it hard to accept that 2000 was the last year of the same century as 1999: the 20th (!) Century. Go figure. https://t.co/pf2GzQc3Ij
— Chris Maslanka (@ChrisMaslanka) January 1, 2020
Primera hora π del año
2020=(3+1)(4+1)(5+92+6)-(5+3)×5#πLife
Expresión vía @Connumeros pic.twitter.com/1PE8JDMQfb
— Juan Miguel Ribera (@juanripu) January 1, 2020
Last blog for 2019! Here are twenty #math puzzles to kick off 2020. Difficulty and subject topics vary. I’ve got counting, arithmetic, #algebra, probability, geometry, #statistics, and a little evil number theory. Enjoy and Happy New Year!https://t.co/h4cliBgyuU#mtbos
— M Shah (@shahlock) January 1, 2020
How mathematicians count down to 2020. https://t.co/55Ek9ZK0ae pic.twitter.com/4PyOb3GWGn
— Cliff Pickover (@pickover) January 1, 2020
2020 can be written as MMXX … What is the next year that can be written as two different Roman Numerals.
What would be a useful starting point? https://t.co/cO7P4k7Ydb…
Download on our FREE resources page#ShowYourWorkingOut ✍️ pic.twitter.com/yb4VMqinSx
— Complete Maths (@LaSalleEd) December 31, 2019
Happy 2020 pic.twitter.com/DeiRECIOSK
— . (@Expert_Says) January 1, 2020
— Dan McQuillan (@normalsubgroup) January 1, 2020
Happy New Year!
2020 is the sum of the squares of four consecutive prime numbers. Can you find them?— Math In The News (@MathInTheNews) December 31, 2019
2020 Mathematics Game — Join the Fun! https://t.co/xYLt3bEPP2
— Math 4 Everybody (@Math4Everybody) January 1, 2020
あってるはず…… pic.twitter.com/cox3UczSeX
— Kei (@Kei21104367) December 31, 2019
— raer (@Jukenkiero) December 31, 2019
— マカロニサラダ (@yosuke8vc) December 31, 2019
— 神崎 月桂／文詠(あやよみ)@嘘創夢想 82569/180000 (@kanzaki_narou) December 31, 2019
— ショショの奇妙な妄言 (@OgunosuShopan) December 31, 2019
2020年01月01日令和02年にちなんで
今年もよろしくお願いします👐 pic.twitter.com/MQ4bTWnwoP
— たっつぁん (@Wz7rNf) December 31, 2019
— U (@u15559) December 31, 2019
やっとできた… pic.twitter.com/RywJ8TyyyL
— たくれ (@tackrei_) December 31, 2019
— こ (@kinsei0916) December 31, 2019
Me han enviado una felicitación de año nuevo cualquier cifra
(1111-111+11-1)x(1+1) =
2222-222+22-2 =
3x((3!)!-33)-33-3×3+3:3 =
4^4x(4+4)-44+4×4 =
5^5-555-555+5 =
((666+6+6:6)x(6+6+6)+6):6 =
(7×7-7-7:7)x7x7+7+7-(7+7+7):7 =
88x(8+8+8)-88-8×8:(8+8) =
999+999+9+9+(9+9+9+9):9 =
2020 https://t.co/BEJDf948qs— Juan Miguel Ribera (@juanripu) January 1, 2020
No habrá otro año con cuatro cifras escrito en números romanos hasta el 2040 #ChristMaths #MathLife https://t.co/RsJ35xdc8v
— Juan Miguel Ribera (@juanripu) January 1, 2020
— マカロニサラダ (@yosuke8vc) December 31, 2019
2020 written as a palindromic, ambigrammatic, strobogrammatic, vertically and horizontally symmetric, ʇuoɹɟ oʇ ʞɔɐq puɐ spɹɐʍʞɔɐq uʍop ǝpᴉsd∩ expression. #HappyNewYear #HappyNewYear2020 #maths #math pic.twitter.com/ryXulOMb60
— Maths Ed (@MathsEdIdeas) January 1, 2020
Because the ratio proportion between the sides of the blue triangles is 1:2, the crossing line is a height of the big triangle, so the baricenter.
Then the rectangle ratio is 1:4 & the side is 4•505=2020 😄 pic.twitter.com/44ngSFPFRg— Guillem Bonet (@willhek1) December 31, 2019
2020 a partir de los 9 primeros números naturales https://t.co/OIFj4iRP9F vía @matescercanas
— emilio lindosa lucas (@411emilio) January 2, 2020
2020 In Numbers – Mathematical Style https://t.co/QKWV1pGUaV pic.twitter.com/IQdvDYHB7w
— INDER J. TANEJA (@IJTANEJA) January 2, 2020
02/02/2020 is the first date to be palindromic across formats (since 11/11/1111). It is the 67th of 335 palindromic ddmmyyyy dates between 10/01/1001 and 29/09/9092, and the 47th of 331 palindromic mmddyyyy dates between 10/01/1001 and 09/29/9290. #HappyNewYear2020 #maths #math pic.twitter.com/5LfMpiR8qJ
— Maths Ed (@MathsEdIdeas) January 3, 2020
2020 In Numbers: Mathematical Style https://t.co/HgV8ipdO35 pic.twitter.com/AeafvSODqv
— INDER J. TANEJA (@IJTANEJA) January 2, 2020
Seguimos con algunas curiosidades sobre el 2020, el año que hemos comenzado. En este caso os traigo ocho ternas pitagóricas de las que forma parte el 2020.https://t.co/w6yPtDSvzN#Bienvenido2020 #Hola2020 #FelizViernesATodos pic.twitter.com/Sen2Qy9aFG
— MatematicasCercanas (@matescercanas) January 3, 2020
Happy New Year! How many pairs of positive integers a and b fit this equation? #maths #puzzle pic.twitter.com/dsbY1tP7oJ
— Puzzle Critic (@puzzlecritic) January 5, 2020
— vivekanand mandal (@vivekanandman16) January 5, 2020
Gave the following challenge to #rdcrs students…
Using each number 1 – 10 exactly once, determine an equation that equals 2020.Here is what 2 students from @STFWolves came up with..
and other examples as well#mathchat #MTBoS pic.twitter.com/HDRlxjzA0P— 𝘋𝘢𝘷𝘦 𝘔𝘢𝘳𝘵𝘪𝘯 (@d_martin05) January 7, 2020
Heart: Mathematics Lovers – Magic Squares of Order 4 of Equal Magic Sums https://t.co/AHhYfZOQwb pic.twitter.com/04AfM5BgfB
— INDER J. TANEJA (@IJTANEJA) January 8, 2020
Shiver in ecstasy. We live in a year that is the sum of the squares of four consecutive prime numbers. pic.twitter.com/R4o3gMZieH
— Cliff Pickover (@pickover) January 14, 2020
Is there any other way to write 2020 as a difference of two squares?
Note: We are looking for a difference of squares of positive integers. Squares of negative numbers and non-integers don’t count! pic.twitter.com/Jbr2UhWSb3
— Brilliant.org (@brilliantorg) January 18, 2020
That’s a lot of love for the number 2020. Have a wonderful year, everybody!