Thanks “Schoko-Streich” lösten Forscher 400 Jahre altes mathematisches Rätsel

If there is a mathematical way of thinking, I think that people often write, think and write with a colored marker on a blue paper. In many cases this Vorstellung wohl auch zu. But things were different for Paul Chaikin, who died at Princeton University in the 2000s: She started with a 200-liter fass fuller of Schokolinsen.

Chaikin is a physical physical activity that focuses on the packaging of objects – a well-known geometry problem. It takes over 400 years for the operating system to be used, which means I have sparse pile welds in most places. As a Physiker file, there are no formal mathematical calculations involved. There are many practical problems, where the small problems are solved in a large number of cases, and herausfinden, who finds the object in a certain case situation.

Auch diese Frage hatte Fachleute in der Vergangenheit beschäftigt. So the British theologian Stephen Hales in 18. Jahrhundert analyzed the zufällige anordnung von Kugeln during experiments with erbsen. The complete human being has entered into a situation, and a larger top, can be obstructed by the hand, and the experience will express itself in a fluid movement. Condenses the human being when he hinges, it will be incomprehensible: the human being can no longer place his hand at the top of the device. It’s a piece of cake phase. Once you find a solution, drop Hales the Hülsenfrüchte with Wasser, but it will dry up. So it is one of the pressure choices that can solve the possibilities of the problem and disappear quickly, which can lead to good order.

Hales’ Experiment is an initiative of the challenging students Evan Variano and. Denn Solche Prozesse plays an important role in the party and material physics. There is an amorphous celebration with glass or granular substances that consist of small components, which allows them to become increasingly organized and exist in different phases (party and fluid zum Beispiel). Delete Variano for an absolute benefit from the effects of reproduction.

The power of the student is also one of the possibilities, Schüttete Erbsen in Behältnisse and overbergoss sie with Wasser – thus, who Hales is described with. But the Erbsen did not move through the flow at all. Whoever Chaikin später herausfand, the Hülsenfrüchte inzwischen was so sighed that they are not aufquellen. The professor must also find an alternative for his students. And if anything, it’s a matter of whichever Arbeitsgruppe wears its hat.

Chaikin’s Labor War at the university for the struggle against the struggle and the efforts. A woman researching labor through Ziegelsteine; am Tag der Geburt von Chaikins erster Tochter who suffices the Labor with Luftballons full; and if you want to use the electricity in the office like this, if you turn off the bell, you can use the telephone abnahm. When the Tag started, while the students and students were choking a 200-liter fass full of M&M’s chocolates in Chaikins Büro, weil esch dabei one of the lying cases in the business of professors, who play their leading role in their Mittagessen. This Fass-inspired Chaikin is a new model for Variano.

Mathematics has acquired a perfect line shape, Mathematics speaks of rotation ellipsoids. Chaikin wies Variano daher an, zu untersuchen, wie ich die Objekte natürlicherweise in Gefäßen anordnen.

Schokolinsen fell more sparingly than Kugeln

Schüttet man Kugeln ungeordnet in einen Behälter, then full sie de Raum zu etwa 64 Prozent aus. Das heißt, etwa 36 Prozent des Behälters ist Leerraum. Der Gelehrte Johannes Kepler was prepared at 17. Years, because I am the closest pack and weld, wenn man who is in a single obstacle with a pyramid shape over a different shape. In a solchen Anordnung vol die Kugeln 74,04 Prozent des Raums aus – als zehn Prozent mehr, als wenn man sie disordered in a Behältnis kippt. When the end of its lifespan has been reached, this seal is tight, but lasts a long time. In 1997, the love of the mathematician Thomas Hales (another Hales, not with the Erbses) with Hilfe was based on the computer.

That Wissen in the Hinterkopf started Variano, the selection of M&M linsen that no longer existed. There is a chain that plays a big role at Kugeln – it was a matter of 64 percent. If the professor informed the Messwerte, he said that it is sceptical. »I no longer have the Ergebnissen glazed and a schließliche self-made gemstones«, said Chaikin in a press conference in 2004. »A natural hatte Evan is right: It is more densely packed.« Tatsächlich is full of the arbitrariness geschichteten Schokolinsen with Varianos Versuchen etwa 71 Prozent des Raums – fast for an optimally organized Kugeln. »Das hat uns umgehauen«, erzählte Chaikin. No one has a problem packing packages.

There is a problem in materials mathematics that plays an important role. Including by Chaikin, leistungsfähige Keramiken rezustellen, indem there Pulver from winzigen Partikelen miteinanderschmolz. A denser package packaging is a very good way to make ceramics, we will find the features of the packaging unobtrusive forms for the Forscher sehr interesting.

Chaikin wants to move on, where Schokolinsen were packed closer than Kugeln. It is necessary that the rotation ellipsoid is turned off. It is also possible to do an examination with Shockolinsen in the medical college of Princeton University and make an MRT scan. Let his student Ibrahim Crisse Farbe in the Schokolinsen-Behälter (of course, if he is no longer in the MRT war) suffice. If you get into a rock net war, the student will have the Linsen heraus and zählte the punker’s jewelry on the right side – if the contact point is from Linsen. Criss said that they are welcome at the Contact Point fest, and are welcome in the Rules for Contact Points. A computer model written in an Ansatz entwickelten der Chemiker Salvatore Torquato together with his students Aleksandar Donev, which simulates the various shapes, including rotational ellipsoids.

Due to these independence relationships and the colleges and colleges that exist, Schokolinsen is marketed as often as Kugeln. If you use a form, there will be a small Hebel, which you can use, while other Linsen dream, when man becomes full in a Behältnis. This Drehung destabilizes the Anordnung. Information about the objects that come closer together before they are lost. If you hinge differently: you can no longer dream and create images that are soft and stable.

Ellipsoid welds do not pack more tightly

Due to the computer model that the computer can use, it is possible for other forms to be adjusted – and ellipsoid. This is a form of shock, but that is not the case. We also got a view of the Kreis that is Schokolinsen, under an Ellipse. Wie de Forschenden herausfanden, ordnen sich Ellipsoide noch poet, when man is in a Behältnis-schüttet: Sie full bis 74 Prozent des Raums aus. Damit since Ellipsoide in zufälligen Packungen fast genauso densely packed with optimally arranged Kugeln. There is a further exceedance of the fachleute.

In the following years, which were on a different part of the Frage, the dense packaging of Ellipsoiden was his property. But neither is there an end-generous Antwort aus. If you change the Ellipsoid anordnungen, the optimal Candidates become gilts and a erstaunliche Dichte of 77 Prozent aufweisen. Another product may not last nearly as long as the welding time – when using the optimal package packaging, this is only more than 400 years ago.