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  1. Thread: The PI Thread

    by lpetrich
    Replies
    34
    Views
    629

    The calculus-based formulas also use...

    The calculus-based formulas also use trigonometric functions, though often indirectly.

    Let's take a closer look at them. Here is a geometric definition of them:

    Consider triangle ABC in a...
  2. Thread: The PI Thread

    by lpetrich
    Replies
    34
    Views
    629

    Mathematica source code: (* Cosine...

    Mathematica source code:


    (* Cosine half-series *)
    cshfser[ni_,nf_:N] := Rest[NestList[Sqrt[(nf[1]+#)/2]&,0,ni]]

    (* Accumulated product *)
    prdaccum[xser_] := Module[{prod=1},...
  3. Thread: The PI Thread

    by lpetrich
    Replies
    34
    Views
    629

    Here is another trigonometry-based formula for...

    Here is another trigonometry-based formula for pi:

    Vieta's Formula for Pi - ProofWiki
    Viète's formula

    pi = 2 * (2/sqrt(2)) * (2/sqrt(2 + sqrt(2))) * (2/sqrt(2 + sqrt(2 + sqrt(2)))) * ...
    ...
  4. Replies
    698
    Views
    31,874

    AOC, 'Squad' members promote 'Defund the Police'...

    AOC, 'Squad' members promote 'Defund the Police' but spend thousands on private security | Fox News - "Bush has spent the most on security services so far this year"

    As self-styled...
  5. Replies
    798
    Views
    15,160

    Poll: Responding to AOC, Derec, do you really think...

    Responding to AOC,

    We live in a dangerous world and defense is a necessity.
    [/quote]
    Derec, do you really think that we Americans live in a war zone? Also, do you really want to promote...
  6. Thread: The PI Thread

    by lpetrich
    Replies
    34
    Views
    629

    Mathematica source code: (* Given a number...

    Mathematica source code:


    (* Given a number and a tangent, fill out the record *)
    fillrec[nm_,tg_] := Module[{sn,cs},
    cs = 1/Sqrt[1+tg^2];
    sn = cs*tg;
    {nm,sn,cs,tg}
    ]
  7. Thread: The PI Thread

    by lpetrich
    Replies
    34
    Views
    629

    Archimedes's algorithm as Euclid-style geometry:...

    Archimedes's algorithm as Euclid-style geometry:

    For circle C and number of polygon sides n, construct two n-gons. An inner one that touches the circle, an inscribed one P. An outer one that also...
  8. Thread: The PI Thread

    by lpetrich
    Replies
    34
    Views
    629

    I think that the oldest known algorithm for...

    I think that the oldest known algorithm for calculating pi is Archimedes's algorithm.

    It uses the inequality
    sin(a) < a < tan(a)
    where a is in radians, and is between 0 and pi/2.

    Start with...
  9. Replies
    798
    Views
    15,160

    Poll: I like this: Alexandria Ocasio-Cortez on...

    I like this:
    Alexandria Ocasio-Cortez on Twitter: "That a family had to lose a son, brother and father; that a teenage girl had to film and post a murder, that millions across the country had to...
  10. Ilhan Omar on Twitter: "🤣🤣 (pic link)" / Twitter...

    Ilhan Omar on Twitter: "🤣🤣 (pic link)" / Twitter
    with picture quote


    Austin Brown on Twitter: "@IlhanMN I love this pic of you. I can imagine its the look and laugh you gave when reading Charlie...
  11. Replies
    127
    Views
    2,886

    Some snippets from that GND-reintroduction press...

    Some snippets from that GND-reintroduction press conference.

    NowThis on Twitter: "Rep. @AOC reintroduces the Green New Deal: ’The climate crisis is a crisis born of injustice and it is a crisis...
  12. Replies
    4,927
    Views
    357,832

    AOC was one of least effective members of...

    AOC was one of least effective members of Congress: study
    That's according to
    The ‘Do-Something’ Members of 116th Congress: Legislative effectiveness study from Vanderbilt, UVA identifies member...
  13. Replies
    4,927
    Views
    357,832

    Alexandria Ocasio-Cortez on Twitter: "Ever wonder...

    Alexandria Ocasio-Cortez on Twitter: "Ever wonder what a Representative does in a week, anyway?
    Here’s what I‘ve been up to since Monday ⬇️" / Twitter
    Ryan Sheales on Twitter: "Here’s another 90...
  14. Replies
    4,927
    Views
    357,832

    Then a 7-year-old constituent asked about why she...

    Then a 7-year-old constituent asked about why she ran for office, how she got into office, and how she copes with people who dislike her. She laughed and said that it is a great question.

    She...
  15. Replies
    9
    Views
    358

    QAnon mentions the hypothesis that there is more...

    QAnon mentions the hypothesis that there is more than one "Q".

    QAnon's Mysterious Leader 'Q' Is Actually Multiple People
    noting
    Style analysis by machine learning reveals that two authors likely...
  16. Replies
    127
    Views
    2,886

    AOC’s plan for a 1.5 million-strong Civilian...

    AOC’s plan for a 1.5 million-strong Civilian Climate Corps, explained | Grist

    "A new bill would bring back FDR's famous New Deal program — with a few big changes."

    There are four features that...
  17. Thread: RussiaGate

    by lpetrich
    Replies
    3,173
    Views
    150,598

    Judge orders Justice Dept. to release Donald...

    Judge orders Justice Dept. to release Donald Trump obstruction of justice memo - ABC7 Los Angeles

    Barr memo saying not to charge Trump must be released, judge says - CNNPolitics

    Redacted...
  18. Replies
    1,793
    Views
    74,029

    Michael Cohen on Giuliani's legal fees: He won't...

    Michael Cohen on Giuliani's legal fees: He won't get 'two cents' from Trump | TheHill
    noting
    Michael Cohen On Giuliani: ‘He’s Going To Get Stiffed’ | The ReidOut | MSNBC - YouTube


    Giuliani...
  19. Replies
    284
    Views
    12,433

    The members of these families whose political...

    The members of these families whose political careers have survived have all had to become Trumpies, even if it means breaking with the rest of their families.
  20. Replies
    284
    Views
    12,433

    He also targets a Republican that many of his...

    He also targets a Republican that many of his fellow Republicans consider a great hero, and someone that they follow.

    Trump: People would say I'm 'far greater than Ronald Reagan' if my name...
  21. Replies
    284
    Views
    12,433

    How Trump is hunting down the GOP’s leading...

    How Trump is hunting down the GOP’s leading families - POLITICO

    Trump was born on 1946 Jun 14, and that means that he was in his early 20's in the late 1960's. His adult years thus overlap with...
  22. If he has any sense of humor, he might respond...

    If he has any sense of humor, he might respond "Ribbit ... ribbit ... ribbit ... I croaked."

    More seriously, there would likely be a big fight over Trump's legacy, with some Republicans claiming...
  23. Replies
    17
    Views
    347

    Trump spokesman says defeating Cheney a top...

    Trump spokesman says defeating Cheney a top priority | TheHill

    Liz Cheney plans lengthy fight over Trump's dominance of Republicans. - The Washington Post

    Like refusing to accept some very...
  24. Replies
    95
    Views
    4,271

    "Fox News made me do it" Lawyer for accused...

    "Fox News made me do it"

    Lawyer for accused Capitol rioter says client had 'Foxitis,' 'Foxmania' | TheHill

    Right-wingers like to talk about taking responsibility for their actions. But when...
  25. Replies
    70
    Views
    2,505

    Amy Vilela on Twitter: "We're officially...

    Amy Vilela on Twitter: "We're officially launching our first campaign video! ..." / Twitter

    Amy Vilela - Ballotpedia lists her as running in NV-01. She ran in NV-04 back in 2018. Her campaign...
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