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✔️¿ MIEDO, FALTA DE MOTIVACIÓN, BAJA AUTOESTIMA? 10 MEJORES TÉCNICAS DE PNL PARA TRANSFORMAR TU VIDA. INFÓRMATE 😃 ▶️ ◀️ Pablo Montesinos




👩‍👧‍👦Within the last year, 165,782 peace letters written by youth globally have been sent to 193 presidents at the as part of International Peace Youth Group () 'Peace Letter Campaign'✌️ 👉




¿TU TAMBIÉN QUIERES SER EXITOSO? DESCUBRE CÓMO EN SOLO 21 DÍAS 🎺🏆👏👏ENTRA AQUÍ ▶️ ◀️ Pablo Montesinos elaearnig




✔️¿ MIEDO, FALTA DE MOTIVACIÓN, BAJA AUTOESTIMA? 10 MEJORES TÉCNICAS DE PNL PARA TRANSFORMAR TU VIDA. INFÓRMATE 😃 ▶️ ◀️ Pablo Montesinos




¿TU TAMBIÉN QUIERES SER EXITOSO? DESCUBRE CÓMO EN SOLO 21 DÍAS 🎺🏆👏👏ENTRA AQUÍ ▶️ ◀️ Pablo Montesinos elaearnig




✔️¿ MIEDO, FALTA DE MOTIVACIÓN, BAJA AUTOESTIMA? 10 MEJORES TÉCNICAS DE PNL PARA TRANSFORMAR TU VIDA. INFÓRMATE 😃 ▶️ ◀️ Pablo Montesinos




¿TU TAMBIÉN QUIERES SER EXITOSO? DESCUBRE CÓMO EN SOLO 21 DÍAS 🎺🏆👏👏ENTRA AQUÍ ▶️ ◀️ Pablo Montesinos elaearnig




✔️¿ MIEDO, FALTA DE MOTIVACIÓN, BAJA AUTOESTIMA? 10 MEJORES TÉCNICAS DE PNL PARA TRANSFORMAR TU VIDA. INFÓRMATE 😃 ▶️ ◀️ Pablo Montesinos




¿TU TAMBIÉN QUIERES SER EXITOSO? DESCUBRE CÓMO EN SOLO 21 DÍAS 🎺🏆👏👏ENTRA AQUÍ ▶️ ◀️ Pablo Montesinos elaearnig




✔️¿ MIEDO, FALTA DE MOTIVACIÓN, BAJA AUTOESTIMA? 10 MEJORES TÉCNICAS DE PNL PARA TRANSFORMAR TU VIDA. INFÓRMATE 😃 ▶️ ◀️ Pablo Montesinos




¿TU TAMBIÉN QUIERES SER EXITOSO? DESCUBRE CÓMO EN SOLO 21 DÍAS 🎺🏆👏👏ENTRA AQUÍ ▶️ ◀️ Pablo Montesinos elaearnig




✔️¿ MIEDO, FALTA DE MOTIVACIÓN, BAJA AUTOESTIMA? 10 MEJORES TÉCNICAS DE PNL PARA TRANSFORMAR TU VIDA. INFÓRMATE 😃 ▶️ ◀️ Pablo Montesinos




¿TU TAMBIÉN QUIERES SER EXITOSO? DESCUBRE CÓMO EN SOLO 21 DÍAS 🎺🏆👏👏ENTRA AQUÍ ▶️ ◀️ Pablo Montesinos elaearnig




✔️¿ MIEDO, FALTA DE MOTIVACIÓN, BAJA AUTOESTIMA? 10 MEJORES TÉCNICAS DE PNL PARA TRANSFORMAR TU VIDA. INFÓRMATE 😃 ▶️ ◀️ Pablo Montesinos




¿TU TAMBIÉN QUIERES SER EXITOSO? DESCUBRE CÓMO EN SOLO 21 DÍAS 🎺🏆👏👏ENTRA AQUÍ ▶️ ◀️ Pablo Montesinos elaearnig




✔️¿ MIEDO, FALTA DE MOTIVACIÓN, BAJA AUTOESTIMA? 10 MEJORES TÉCNICAS DE PNL PARA TRANSFORMAR TU VIDA. INFÓRMATE 😃 ▶️ ◀️ Pablo Montesinos



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Taking vacation stirs up thoughts of a new show on Pi Day. 😒 #piday2019 #piday #vacation #sexshow #focus #arizona #comedy #talk #radio #show #fatguyradioshow #internetradio #men #dude #podcastlife (at Glendale, Arizona)
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In Which Archimedes is Abducted by Aliens

So in honor of pi day (it’s always pi day somewhere probably), regarding Archimedes’ famous upper bound of pi of twenty-two sevenths and less famous lower bound of two hundred and twenty-three seventy-firsts.  This came from his use of two enneacontahexagons, one on the outside, one on the inside.  However, what if you don’t have access to geometry, what if you only know pi as the lowest strictly positive zero of the sine function (yes I have been on a certain website)?  Well, then, you could approximate Archimedes method by showing that that upper bound is less than ninety-six times the tangent of a ninety-sixth pi, and that that lower bound is greater than ninety-six times the sine of a ninety-sixth pi.  But how do you establish that these are on opposite sides of pi?

Well, first, how does Archimedes?  How does Archimedes even assert that a circle has an arclength?  Well, how would we define it now?  By the integral of the lengths between nearby points, essentially, treating this as a Riemann mesh.  That’s pretty much what the inner polygons represent, but also they can be seen as an appropriate lower bound by the notion that a straight line is the shortest between two points, which is as good a first principle as any.  It can then be shown that the outer polygons are a least upper bound since they get arbitrarily close and never less.  Consistency’s not shown, but it never can be.

This raises the question of what exactly the Euclidean distance is, since even this notion of arclength depends on it.  Of course, normally, the Pythagorean theorem is assumed as naturally as breathing.  Those of a certain persuasion will tell you the Pythagoreans “stole it from brown people,” meaning that Egyptians and Babylonians had the use of it, although no extant proof.  They can’t have cut it from whole cloth, though, so let’s ask ourselves - what exactly is the Pythagorean theorem?

Well, let’s look at what’s sometimes called the “Pythagorean proof,” one more visually obvious than Euclid’s - four equal right triangles, arranged first into two rectangles that leave two squares, then into a frame of a square on the hypotenuse.  Note that both of these form a square of side equal to the sum of the two legs, which can be broken down by algebra.  So in essence the proof is the proof of the existence of triangles; in the Euclidean distance, including in arclength, is hidden the abstract notion of the triangle.

But returning to Archimedes how to show from this alternate notion the boundaries on this zero of the sine?  What’s to be shown is that, just above zero, the sine is always less and the tangent always greater.  That the sine is always less can be seen from the series representation, at least for a sufficiently small parameter.  That the tangent will be greater can be seen by multiplying the series expansion of the cosine by the parameter and subtracting to see that the sine will be greater near zero.

From there you just need the half-angle formulas, although that’s not what he himself uses.  For the tangent, he uses the fact that if you bisect an angle, the ratio of the lengths of the base are that of the sides.  For the sine, he uses the same twice.  Algebraic manipulation of the half-angle formulas will give a similar result probably and I hear birds.

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#Repost @usarmy
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Today is #PiDay. For all you math fans out there, how many digits of Pi can you count to?

Video by Spc. Julie Driver

#math #education #STEM #314
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Memories from last years π day - I think of it as Thanksgiving in March. A solid reason to eat pie. #memoriesofpi #calgarybuzz #calgarybakery #calgaryeats #instapies #shoplocalyyc #eatlocal #piday #pi #pie #pies #π #πday #mathgeek #mathematics #mathmemes #yycbuzz #yyceatsnow #calgaryalberta #calgarynow #calgarybuzz
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Pi Day Stuff

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Pi Day

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Pi Day Stuff