Summer Days, and Coming Soon: Maker Club!

Vine Preparatory Academy

As unschoolers and members of a loose affiliation of home and unschool educators, we keep a year round schedule. Sometimes though, the changing season begs to be marked and celebrated.

Are you celebrating or changing your learning activities in any particular way for summer?

For Vine Preparatory Academy this summer is all about that beach- every Wednesday. Nature is calming, comforting and intrinsically educational for the kids. Our cohort offers weekly activities year round, but they will have to fit in around those beach trips. Well, and weekly gaming days too- no Vine Prepper is going to let game day go by the wayside, and you can take that to the bank.

So. Beach and game day weekly, all other activities optional.

A relaxed schedule gives Vine Preparatory Academy time to work through two key strategic and tactical thought and implementation processes.

It’s actually all about that STEAM, right? Science, Technology…

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The hydrostatic forces on an aquarium !

M Dash Foundation: C Cube Learning

Calculus

Manmohan Dash, g6pontiac@gmail.com

An aquarium 2 m long, 1 m wide, and 1 m deep is full of water. Find

(a) The hydrostatic pressure on the bottom of the aquarium,

(b) The hydrostatic force on the bottom, and the hydrostatic force on one end of the aquarium.

Answer;

(a) The hydrostatic pressure on the bottom is obviously ρgh where ρ = 1000kg/m³ and g = 10ms². Also h = 1m. So P = ρgh = 1000 × 10 × 1 = 10000 Pa. Pa = Pascals; SI unit of pressure.

(b) Now the force on bottom is F = P × A = 10000 × 2 × 1 = 20000 N, where SI unit of force is Newton (N).

For the force on the end of the aquarium we need to take each layer of side wall, as the pressure varies with depth. So F = P × A = ∫¹ρ.g

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Forty

aspiblog

INTRODUCTION

This is a different post from my usual style – there will be no pictures, and just the one link which I feel must be shared and which will feature at the end of the post.

FORTY

It is inevitable when writing about the number 40 that there will be considerable overlap with the detail contained in Derrick Niedermann’s wonderful book Number Freak but I hope that some of the stuff I come with is new. One of the things Niedermann talks about is the use of forty in ancient times to denote ‘a large number’ in which he context he mentions various biblical references and the tale of Ali Baba and the Forty Thieves – which reference particularly appeals as I am the proud owner of both a four volume boxed set of the complete 1,001 nights and a Folio Society edition of the highlights.

SOME OF THE…

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An “A” For An “I”

Selections from the First Hundred Stellations of the Rhombicosidodecahedron

RobertLovesPi.net

Since shortly after I learned of their existence, I have found the rhombicosidodecahedron to be the most attractive of the Archimedean solids. That’s a personal aesthetic statement, of course, not a mathematical one.

This solid has a long stellation-series. With Stella 4d, the program I used to make these images, it’s easy to simply scroll through them. The stellation of this polyhedron follows these stellation-diagrams; I used Stella 4d to make them as well. You may research, try, or buy this program at this website. The first of these stellation-diagrams is for the planes of the twelve pentagonal faces.

For the planes of the twenty triangular faces, this is the stellation-diagram:

Finally, there are the the planes of the thirty square faces.

The following survey of the first hundred stellations is not intended to be exhaustive; I’m including all those I find worthy of inclusion on subjective aesthetic…

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Selections from the Second Hundred Stellations of the Rhombicosidodecahedron

RobertLovesPi.net

This survey began in the last post, with selections from the first hundred stellations of this Archimedean solid. In this survey of the second hundred stellations, the first one I find noteworthy enough for inclusion here is the 102nd stellation.

A similar figure is the 111th stellation:

There followed a long “desert” when I did not find any that really “grabbed” me . . . and then I came to the 174th stellation.

The fact that it is monocolored, the way I had Stella 4d set, told me immediately that this stellation (the one above) has only one face-type. There are twenty of these faces; they are each equilateral hexagons which “circumscibe,” in a way, the triangular faces of an icosahedron. For this reason, I suspect this is also one of the stellations of the icosahedron; I’m making a mental note to do exactly that.

I also make a second…

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Realistic Bouncing ball animation

Muddassir Ahmed's Blog

http://www.khanacademy.org/computer-programming/bouncing-ball/4634234574733312

****************************************Code********************************************

// position of the ball
var y = 100;
// how far the ball moves every time
var acceleration=2;
var speed = 0;
var ballR=18;
var prevY=100;

var draw = function() {

background(206, 196, 255);
noStroke();
fill(44, 138, 51);
ellipse(200, y, ballR, ballR);
if(y>=(400-ballR/2))
{
speed=-speed;
if(prevY>y)
{
acceleration=0;
speed=0;
y=400-ballR/2;
}

}
if(speed===(speed-2))
{
acceleration=0;
}
if(y<=100)
{
y=100;
speed=0;

}
speed+=acceleration;
// move the ball
prevY=y;
y += speed;
mouseClicked=function(){
y = 100;
acceleration=2;
speed = 0;
ballR=18;
prevY=100;
};
};

*****************************************END*******************************************

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Nigerian Student Solves 30 Year Old Math Equation

Dark Matters

Breaks Academic Record at Japanese University

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Cubic curves

Renaissance Universal

The reason I am interested in cubic curves is that they may be the simplest mathematical representations of the twisting action.

In “Prometheus and Chronos” I tried to build a conceptual model of particles based on the hypothesis of intrinsic flow in curved primordial threads. The curvature is the result of a symmetry breaking that I refer to as the “twisting action.”

As a result of the twisting action a multitude of curved forms of the fundamental thread are possible. Let us consider the simplest form shown in the figure below. Note the 2 semi-circles and the flow direction as indicated by the arrows. The primordial flow shown by the arrows is intrinsic.

Why is there a “twisting action” in the first place? This question cannot be answered in the context of physics. Mystery will remain but the progress will be measured by the economy of our theory. The simplest and…

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Show it what for…