Thursday 29 November 2012

Thales theorem

A very funny way of explaining Thales Theorem:

Dividing a segment into several equal parts
We use Thales theorem to divide a given line segment into a number of equal parts with compass and straightedge or ruler.  By using a compass and straightedge construction, we do this without measuring the line.

I think my construction is easier, but here you have another construction. In the applet we divide it into five parts but it can be any number. You will discover that both are the same!.

Simple elements

POINT
A precise location or place on a plane. Usually represented by a dot, a cross or an x. Since a point is a place, not a thing, it has no dimensions.

LINE
A geometrical object that is straight, infinitely long and infinitely thin. A line is one-dimensional. It has zero width. Using two points, we can create only one line.
In the figure above, the line PQ passes through the points P and Q, and goes off in both directions forever, and is perfectly straight. A line, strictly speaking, has no ends.

VERTICAL AND HORIZONTAL LINES
A vertical line is one which runs up and down the page.
A horizontal line is one which runs left-to-right across the page. It comes from the word 'horizon', in the sense that horizontal lines are parallel to the horizon.
horizon

RAY
A portion of a line which starts at a point and goes off in a particular direction to infinity. One way to think of a ray is a line with one end. The point where the ray starts is called the endpoint. A ray is one-dimensional. It has zero width. A ray has no measurable length, because it goes on forever in one direction.
P is the endpoint

LINE SEGMENT
A straight line which links two points without extending beyond them. A line segment is one-dimensional. It has a measurable length, but has zero width.
P and Q are the endpoints of the line segment y

MIDPOINT OF A LINE SEGMENT
A point on a line segment that divides it into two equal parts. The halfway point of a line segment.

M is the midpoint
P and Q are the endpoints of the line segment

INTERSECTION OF LINES
The point where two lines or two line segments meet or cross.
Animation.
In the figure above we would say that "point K is the intersection of line segments PQ and AB".
Another way it may be said is that "the line segment PQ intersects AB at point K".
PARALLEL LINES
Lines are parallel if they lie in the same plane, and are the same distance apart over their entire length. No matter how far you extend them, they will never meet.
PERPENDICULAR LINES
A line is perpendicular to another if it meets or crosses it at right angles (90°).
Animation.
AB is perpendicular to DF

CIRCLE
A line forming a closed loop, every point on which is a fixed distance from a center point.
There is a difference between a circle and a disk. A circle is a line, and so, for example, has no area - just as a line has no area. A disk however is a round portion of a plane which has a circular outline. If you draw a circle on paper and cut it out, the round piece is a disk.
Radius animation.
Diameter animation.
Arc animation.
Sector animation.
Tangent animation.
Secant animation.


PLANE
A flat surface that is infinitely large and with zero thickness. The plane has two dimensions: length and width. But since the plane is infinitely large, the length and width cannot be measured.

PARALLEL PLANES
A flat surface that is infinitely large and with zero thickness. You can think of parallel planes as sheets of cardboard one above the other with a gap between them. Parallel planes are the same distance apart everywhere, and so they never touch.

The two bases of this cilinder are parallel planes

INTERSECTING PLANES
If two planes are not parallel, then they will intersect (cross over) each other somewhere. Two planes always intersect at a line, as shown on the right.
This is similar to the way two lines intersect at a point.

SOLID GEOMETRY

The basics of geometry

Introduction
Introduction to constructions.  Compass. Ruler. Straightedge. Euclid.

Now, learn and enjoy with these introductory videos:
You will have to learn all these vocabulary. But... don't worry! We will go with it little by little.

POINT - LINE



PARALLEL LINES - CONVERGING LINES - ANGLE - TRIANGLES



ACUTE, RIGHT AND OBTUSE ANGLES - CIRCLE - RADIUS - CIRCUMFERENCE - DIAMETER



SQUARE - DEGREES



EQUILATERAL, ISOSCELES AND SCALENE TRIANGLES.
ACUTE, RIGHT ANGLED AND OBTUSE TRIANGLES.




POLYGONS (Wondeful video using Origami Technique)

Saturday 17 November 2012

Origami

Origami  (折り紙?, from ori meaning "folding", and kami meaning "paper"; kami changes to gami due to rendaku) is the traditional Japanese art of folding paper into a shape representing an object.
There is much speculation about the origin of Origami. While Japan seems to have had the most extensive tradition, there is evidence of an independent tradition of paperfolding in China (traditional funerals include burning folded paper), as well as in Germany, Italy and Spain among other places.

Akira Yoshizawa - Origami master showing us... a  turkey!
Origami tools:
You don’t need any origami tools to fold paper. All you need is your hands, a piece of paper, and a flat surface to fold on. Easy. You can do it at home, you can do it at school (oops, did I really say that?). You can do it on the train, you can do it on the bus. You can do it in a coffee shop, you can do it in a restaurant or...


(see dollar-bill origami and napkin and towel folding).

How to make origami:
There are many folding techniques that you need to learn to form a shape out of a piece of paper. Folding techniques. Two most important techniques are valley-fold and mountain-fold. At least, you must know what they are and you will have no problem of folding a simple origami model by using only these two folding techniques.

Wet folding origami:
Wet folding origami is a relatively new way of folding paper. It was developed by origami master Akira Yoshizawa and it involves moistening the paper before you fold it. The resulting model has a softer, textured look with gentle curving lines.
Gilad’s web site shows the difference between a regular origami dog and a wet fold origami dog. Wow! [Puppy created by Francisco Javier Caboblanco; photo by Gilad Aharoni]


Interesting links for origami:
  • Origami and pop-up books.
  • OrigamiProject. To relax.
  • Origami Maniacs.
  • Last October, I visited 'ESTAMPA ARTE MÚLTIPLE' FAIR which was held in Matadero Madrid. I discovered a new exhibitor: MAATT. Maatt is brand-new company focused on home decoration objects. They exploit the possibilities of any material they find on the way. Their first collection is based on paper and it is called Animaatts, and the best is that it's a do it yourself!, of course, with instructions. I have seen this collection 'in situ' and it looks great!. It is a good example of 'minus is more'.

Thursday 15 November 2012

Discovering ORIGAMI - volume with paper, for Thanksgiving

This will be our second task for Thanksgiving Day. You only need two sheets of white paper to begin practising ORIGAMI

The design requires two sheets of paper. The first is used to make the body. The second sheet is used to make the fanned tail. Is it possible to make the tail in two colors although the paper gets thick and it often slides out of place. Using tissue paper to make the fanned tail allows multiple sheets to be stacked and folded without it getting overly thick.

Kids Turkey

José María V. (1st B) will show us how to create another type of turkey with legs:

Tuesday 13 November 2012

WARM AND COLD COLORS






Saturday 10 November 2012

Discovering WARM AND COLD COLORS

Cold colors                                      Warm colors


We are going to build this cute turkey made from your hadprints and footprints, cut out of construction paper. It will be a very nice Thanksgiving decoration for our Highschool.



Hand and Foot Turkey Craft


More ideas for Thanksgiving Day:


Your tasks: Discovering symmetries


MONSTRUOUS SYMMETRY - 1st A, B and C ESO 2012/2013 on PhotoPeach