I thought it could be nice to use different domains of Mathematica to represent 2023 in different ways.
Outline:
- Entities
- Polynomial algebra
- Linguistic Data
- Number theory
- Text analysis
- Special functions
- Plotting
For the fun of it, here is the outline as an unordered wordcloud with DropShadowing (version 13.1) :
Note : Text placement might differ each time as it is random.
WordCloud[{"Entities", "Polynomial algebra", "Linguistic data",
"Number theory", "Text analysis", "Special functions", "Plotting",
Rotate["2023", Pi/3]}] /.
Graphics[{a_, b___}, c___] :> Graphics[{DropShadowing[], a, b}, c]
Entities
Write 2023 as the approximate ratio between the mass of an exoplanet and that of earth.
Mass of the earth:
earthMass =
Entity["Planet", "Earth"][EntityProperty["Planet", "Mass"]];
The exoplanets that have a mass that is roughly 2023 times that of the earth :
FilteredEntityClass["Exoplanet",
EntityFunction[e,
Abs[e["Mass"]/(2023*earthMass) - 1] < 0.1]] // EntityList
Polynomial algebra
Find an expression for 2023 in terms of radicals.
Using the general formula for a quartic:
sol = Solve[x^4 + a*x^3 + b*x^2 + c*x + d == 0, x];
Considering a random monic polynomial that has root 2023:
coefrule = {d, c, b, a} -> (Drop[#, -1] &)@
CoefficientList[(RandomInteger[{1, 5}, 3] . x^Range[0, 2] +
x^3)*(x - 2023), x] // Thread
Thus another representation of 2023 that most people might be less familar with is :
$$2023=\frac{1}{2} \sqrt{\frac{1}{3} \sqrt[3]{\frac{1}{2} \left(49748794692 \sqrt{705}-1342923812836\right)}-\frac{24470164}{3} (-1)^{2/3} \sqrt[3]{\frac{2}{1342923812836-49748794692 \sqrt{705}}}+\frac{3072436}{3}}+\frac{1}{2} \sqrt{-\frac{1}{3} \sqrt[3]{\frac{1}{2} \left(49748794692 \sqrt{705}-1342923812836\right)}+\frac{1}{3} (-1)^{2/3} 24470164 \sqrt[3]{\frac{2}{1342923812836-49748794692 \sqrt{705}}}+\frac{6144872}{3}+\frac{2072863396}{\sqrt{\frac{1}{3} \sqrt[3]{\frac{1}{2} \left(49748794692 \sqrt{705}-1342923812836\right)}-\frac{24470164}{3} (-1)^{2/3} \sqrt[3]{\frac{2}{1342923812836-49748794692 \sqrt{705}}}+\frac{3072436}{3}}}}+505$$
Linguistic data
Write the year 2023 in some of the most spoken languages.
First find the the top 10 most spoken languages. I used free form with ctrl+= followed by top 10 most spoken languages. After applying EntityList we have:
Unfortunately the code below does not work with a lot of languages so I took the top 20 most spoken an extracted the cases that worked.
languages =
EntityClass[
"Language", {EntityProperty["Language", "TotalSpeakers"] ->
TakeLargest[20]}] // EntityList
Then we use IntegerName to write the year 2023 and we also use Transliterate to write the word in ASCII format:
(
languages
//Map[{CommonName@#,
IntegerName[2023,
"Year",
Language->#]
//{Identity,Transliterate}//Through
//Splice
}&]
//Quiet
//DeleteCases[_?(Not@*FreeQ[_IntegerName])]
)
Unfortunately the output seemed to have errors with east asian languages so I removed those manually. I also used TraditionalForm as it looked nicer.
Curated version
There seems to be an error for the name for 2023 in french (but maybe that is how it is pronounced in Canada not sure). Hence, I changed it in the table below. Upon request I also added Greek. Greek is not given in the dropdown menu when typing a language with IntegerName but it still works with IntegerName[2023, "Year", Language -> "Greek"]. Feel free to leave a comment with the translation in your language.
Number theory
Characterize 2023 as the unique number specifying a number theory related property
2023 is the only lucky number of this decade.
The list of lucky numbers lower than a certain integer can be found using the resource function LuckyNumbers. The list below shows the last 2 before 2030.
ResourceFunction["LuckyNumbers"][2030][[-2 ;; -1]]
(* {2019, 2023} *)
Text analysis
Characterize 2023 as the year where certain events are planned to occur.
One can use the wikipedia page on 2023 :
data = WikipediaData["2023"];
Then we can extract the list of events using:
TextSentences[StringExtract[data, "==" -> 5]]
Bonus: For a given event in that list we can get a data set of text contents using TextContents and we can ask questions about the event from the text content using FindTextualAnswer.
Special functions
Write 2023 as a MeijerG function evaluated on an explicit argument.
Consider a simple function and find the MeijerG representation:
expression=1/(1 + x^2) // MeijerGReduce[#, x] &
Find a value for x where the function is equal to 2023 :
sol = Solve[1/(1 + x^2) == 2023][[1]]
The result :
expression /. sol
$$\text{MeijerG}\left[\{\{0\},\{\}\},\{\{0\},\{\}\},-\frac{2022}{2023}\right]$$
Plotting
Write 2023 as the limit of a sequence and plot that sequence to visualize the limit and accuracy
Consider a continued fraction representation of 2023 as Exp[ContinuedFraction[Log[2023]]]. In the following we will plot the convergence of the sequence u[n]=Exp[ContinuedFraction[Log[2023]],n] using the resource function MultipleAxesPlot.
Visualizing the sequence :
digits = ContinuedFraction[Log[2023], 20];
Table[digits[[1]] +
ContinuedFractionK[(HoldForm /@ digits)[[k]], {k, 2, l}], {l, 1,
7}] // Map[Exp] // Quiet // TraditionalForm
$$\left\{e^7,e^{7+\frac{1}{1}},e^{7+\frac{1}{1+\frac{1}{1}}},e^{7+\frac{1}{1+\frac{1}{1+\frac{1}{1}}}},e^{7+\frac{1}{1+\frac{1}{1+\frac{1}{1+\frac{1}{1}}}}},e^{7+\frac{1}{1+\frac{1}{1+\frac{1}{1+\frac{1}{1+\frac{1}{2}}}}}},e^{7+\frac{1}{1+\frac{1}{1+\frac{1}{1+\frac{1}{1+\frac{1}{2+\frac{1}{1}}}}}}}\right\}$$
Interpolate the sequence and Log10 of the relative error with respect to the limit:
curves =
Exp@Convergents[Log[2023], 20] // {Interpolation,
Interpolation[Log10[Abs[#/2023 - 1]] ] &} // Through;
Plot the sequence using the resource function MultipleAxesPlot:
options = {PlotStyle -> {RGBColor[0.0737601, 0.865914, 0.132145],
RGBColor[0.874018, 0.204385, 0.872946]},
"SecondaryAxesColor" -> RGBColor[0.874018, 0.204385, 0.872946]};
ResourceFunction["MultipleAxesPlot"][Through[curves[x]], {x, 1, 20},
Sequence @@ options]
2023and so doesIntegerPartitions[2023]count? – bmf Jan 01 '23 at 03:17ResourceFunction["RandomIntegerPartition"][2023]– userrandrand Jan 01 '23 at 14:01