Mjue mtaalamu wa Hesabu!!

Nyamgluu said:

Jamaa huyo hapo na kwa wale wenzangu wanaolitaka hilo fumbo ili labda waweze kulifumbua from another approach fumbo lenyewe hili hapa:
[h=3]Poincaré's question[/h] At the beginning of the 20th century, Henri Poincaré was working on the foundations of topology—what would later be called combinatorial topology and then algebraic topology. He was particularly interested in what topological properties characterized a sphere.
Poincaré claimed in 1900 that homology, a tool he had devised based on prior work by Enrico Betti, was sufficient to tell if a 3-manifold was a 3-sphere. However, in a 1904 paper he described a counterexample to this claim, a space now called the Poincaré homology sphere. The Poincaré sphere was the first example of a homology sphere, a manifold that had the same homology as a sphere, of which many others have since been constructed. To establish that the Poincaré sphere was different from the 3-sphere, Poincaré introduced a new topological invariant, the fundamental group, and showed that the Poincaré sphere had a fundamental group of order 120, while the 3-sphere had a trivial fundamental group. In this way he was able to conclude that these two spaces were, indeed, different.
In the same paper, Poincaré wondered whether a 3-manifold with the homology of a 3-sphere and also trivial fundamental group had to be a 3-sphere. Poincaré's new condition—i.e., "trivial fundamental group"—can be restated as "every loop can be shrunk to a point."
The original phrasing was as follows:

Consider a compact 3-dimensional manifold V without boundary. Is it possible that the fundamental group of V could be trivial, even though V is not homeomorphic to the 3-dimensional sphere?
​

Kwa wale ambao mnalalmika hamjaletewa haya maswali do not dispair kuna haya hapa chini bado: Yanaitwa
[h=1]Millennium Prize Problems[/h] [h=2]Contents[/h]

• 1 P versus NP
• 2 The Hodge conjecture
• 3 The Poincaré conjecture (proven)
• 4 The Riemann hypothesis
• 5 Yang–Mills existence and mass gap
• 6 Navier–Stokes existence and smoothness
• 7 The Birch and Swinnerton-Dyer conjecture

Atakaeshinda asinisahau hata ka 5% tu ka prize money.

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• P versus NP by Stephen Cook.
• The Hodge Conjecture by Pierre Deligne.
• The Poincaré Conjecture by John Milnor. (SOLVED).
• The Riemann Hypothesis by Enrico Bombieri.
• Yang-Mills Existence and Mass Gap by A. Jaffe and E. Witten.
• Navier-Stokes Existence and Smoothness by Charles Fefferman.
• The Birch and Swinnerton-Dyer Conjecture by Andrew Wiles.

Manyerere Jackton said:

Watu wote! Hapana. Afrika lilishaletwa?

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Nyamgluu said:

Jamaa huyo hapo na kwa wale wenzangu wanaolitaka hilo fumbo ili labda waweze kulifumbua from another approach fumbo lenyewe hili hapa:
Poincaré's question

At the beginning of the 20th century, Henri Poincaré was working on the foundations of topology—what would later be called combinatorial topology and then algebraic topology. He was particularly interested in what topological properties characterized a sphere.
Poincaré claimed in 1900 that homology, a tool he had devised based on prior work by Enrico Betti, was sufficient to tell if a 3-manifold was a 3-sphere. However, in a 1904 paper he described a counterexample to this claim, a space now called the Poincaré homology sphere. The Poincaré sphere was the first example of a homology sphere, a manifold that had the same homology as a sphere, of which many others have since been constructed. To establish that the Poincaré sphere was different from the 3-sphere, Poincaré introduced a new topological invariant, the fundamental group, and showed that the Poincaré sphere had a fundamental group of order 120, while the 3-sphere had a trivial fundamental group. In this way he was able to conclude that these two spaces were, indeed, different.
In the same paper, Poincaré wondered whether a 3-manifold with the homology of a 3-sphere and also trivial fundamental group had to be a 3-sphere. Poincaré's new condition—i.e., "trivial fundamental group"—can be restated as "every loop can be shrunk to a point."
The original phrasing was as follows:

Consider a compact 3-dimensional manifold V without boundary. Is it possible that the fundamental group of V could be trivial, even though V is not homeomorphic to the 3-dimensional sphere?
​

Kwa wale ambao mnalalmika hamjaletewa haya maswali do not dispair kuna haya hapa chini bado: Yanaitwa
Millennium Prize Problems

Contents

• 1 P versus NP
• 2 The Hodge conjecture
• 3 The Poincaré conjecture (proven)
• 4 The Riemann hypothesis
• 5 Yang–Mills existence and mass gap
• 6 Navier–Stokes existence and smoothness
• 7 The Birch and Swinnerton-Dyer conjecture

Atakaeshinda asinisahau hata ka 5% tu ka prize money.

Click to expand...

MKATA KIU said:

Duh na A zangu za namba za kutosha hii kitu ni noma,, hii haiwezi kuwa hisabati.. Duh sijawai kuona kwa kweli hata kwa kuhisi

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Athumans Lugendo said:

Haya mliokuwa mnalitaka hilo fumbo mufumbue kazi kwenu sasa mi nasubiri tu nione nani atapatia

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njiwa said:

kuna vichwa UDSM vita solve

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