Lauren London Hair Weave Length

Activity solid geometry (second) of

An activity to introduce the representation of solids in perspective and make volume calculations. Initially, students will construct a tetrahedron origami. For this I will show him this little film


and will have a sheet with pictures to do so at their leisure. In passing it may consider to demonstrate that the faces are obtained by folding equilateral triangles. Once folded, the student must identify and calculate the length of the side, the position of the center of the face and height using the Pythagorean theorem. It can thus calculate the volume of the tetrahedron it comes to manufacture. Once manufactured the tetrahedra, the students instructed to assemble tetrahedrons in order to obtain a tetrahedron with dimensions doubled. we quickly realized that it useless to paste the tetrahedra face against face, edge or even against edge, and in fact they should be put on top summit, even if the resulting solid contains a large hole. But what is the shape of this hole? It's hard to see ... Two solutions to better realize: magnetic rods. 1) We remake the four tetrahedra on each other, then removes what is too ... 2) We drew the four tetrahedra in perspective. In passing, we remember the rules: two parallel lines in space are represented by two parallel lines on the drawing. On parallel lines, proportions in length are retained. In going back to red edges of the hole, we realize we have shown an octahedron, and its parallel edges are found in FIG. We arrive at the almost magical part of the activity. What is the volume of the octahedron obtained? Students, surely a bit chilled by the calculation of the volume of the tetrahedron, will go against the grain. And yet! Obtained as the tetrahedron is an enlargement of the small initial tetrahedron with a coefficient 2, the volume has increased by 8. However, there are only four small tetrahedrons. So the full volume is equal to 4 times the initial volume. So the empty part is also 4 times the initial volume. The octahedron has a volume four times larger than the tetrahedron same side. In passing, we can see that the tetrahedron can not pave the area, but the tetrahedron and octahedron pave all the space, as illustrated beautifully in this print by Escher, "Planar".

Images Of A Volleyball Cake

topology superheroes

Topology is a branch of mathematics concerning the study of spatial deformations by continuous transformations (without tearing or gluing of structures). (Wiki) The first
problem that can be connected to the topology of the problem is seven bridges of Königsberg, studied in 1736 by Swiss mathematician Leonard Euler.
Later, in 1895, Henri Poincaré launches first foundations of his work in topology analysis situs and introduces the concept of homology that interests us here. To talk

great popularizer, interest is the number of holes in the volumes. For example, we differentiate the ball (no holes) donut (torus) that has a hole. We will continuously deforms the ball fine, without tearing, it never will obtain the torus, and vice versa. The
topologist will knead, stretch, deform in emulation volumes of rubber to obtain topologically equivalent volumes.

A joke is a topologists topologist confuses a cup with a handle and a donut.


The best teacher of topology that we can dream is Professor Richards, head of the Fantastic Four, also known as Mister Fantastic. A brilliant scientist coupled with a deformable continuous rubber ball is the dream.

In looking for the different manifestations of the powers of the king by Mister Fantastic Jack Kirby, I would argue that Jolly Jack was intuitively understood the concept of topological equivalence. Examples support.

could summarize the power of Reed Richards saying it is topologically equivalent to a ball .

So by continuous deformation, Mister Fantastic can turn into a ball.


He therefore has no hole, and therefore can not be pierced by bullets. In fact, every hole, its topology becomes that of a donut.
And if Red had an ear piercing done before getting his powers, his powers would probably have been changed. He probably could deform and move the hole so that bullets pass through this hole.


So he has two Stategies for an attack by gunfire. Remember bullets continuously deforms its body to accompany their journey or deform so as to avoid (drawing Pollard K)



The ball is topologically equivalent to a block rectangualaire (anyone who has done The pastry can testify) and also bagged (not perforated), which can be handy if you want to capture the Hulk, for example.


To turn it into a torus, Red must pick up its structure, by withholding part of his body with his arms.



In all the episodes of Kirby FF from my collection, I found he respected the continuous deformation and equivalence to the ball. Except for these few exceptions, but I think we can charge them with ink, worse topologists.

In FF11, the two seem to weld arm at the elbow, which would make it equivalent to the torus. This is undoubtedly an error inking, or there was a bubble in place of the error, this error is too coarse to be desired.



In FF14, Mister Fantastic is transformed into a net to capture Namor. The ink seems to give the idea of a volume with many holes:


Fortunately, close up, Kirby explains how to obtain the net while keeping the ball structure. It seems to work better. Would still have to study the net structure using graph theory to be sure.


Even schema in FF17. Kirby seems to drill many holes in the structure of Mr. Fantastic. But it fixes the idea in the following picture showing us his stuff and leaves no doubt: it is a mistake to inking.


I do not think Jack Kirby has held a topology book in his hands, but his intuition of the deformation of a ball was perfectly coherent over the 102 episodes that he has drawn.

But to understand a concept, it may be interesting to have examples-cons, I was told these little monsters multicolored who do not know the topology.