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Gauss and at
While at university, Gauss independently rediscovered several important theorems ; his breakthrough occurred in 1796 when he showed that any regular polygon with a number of sides which is a Fermat prime ( and, consequently, those polygons with any number of sides which is the product of distinct Fermat primes and a power of 2 ) can be constructed by compass and straightedge.
Gauss also discovered that every positive integer is representable as a sum of at most three triangular numbers on 10 July and then jotted down in his diary the famous note: " ΕΥΡΗΚΑ!
In his 1799 doctorate in absentia, A new proof of the theorem that every integral rational algebraic function of one variable can be resolved into real factors of the first or second degree, Gauss proved the fundamental theorem of algebra which states that every non-constant single-variable polynomial with complex coefficients has at least one complex root.
Gauss, who was 23 at the time, heard about the problem and tackled it.
" Four normal distribution | Gaussian distributions in statisticsThis unproved statement put a strain on his relationship with János Bolyai ( who thought that Gauss was " stealing " his idea ), but it is now generally taken at face value.
Grave of Gauss at Albanifriedhof in Göttingen, Germany.
Gauss also upheld religious tolerance, believing it wrong to disturb others who were at peace with their own beliefs.
* The Gauss Haus, an NMR center at the University of Utah,
However, the Theorema Egregium of Carl Friedrich Gauss showed that already for surfaces, the existence of a local isometry imposes strong compatibility conditions on their metrics: the Gaussian curvatures at the corresponding points must be the same.
The most well-known use of the Cooley – Tukey algorithm is to divide the transform into two pieces of size at each step, and is therefore limited to power-of-two sizes, but any factorization can be used in general ( as was known to both Gauss and Cooley / Tukey ).
Other standard iterative methods for matrix equation solutions can also be used, for example the Gauss – Seidel method, where updated values for each patch are used in the calculation as soon as they are computed, rather than all being updated synchronously at the end of each sweep.
When the matter of honorary degrees came up at the University of Göttingen six years after Germain's death, Gauss lamented, “ proved to the world that even a woman can accomplish something worthwhile in the most rigorous and abstract of the sciences and for that reason would well have deserved an honorary degree.
* July 10 – Carl Friedrich Gauss discovers that every positive integer is representable as a sum of at most 3 triangular numbers.
* Carl Friedrich Gauss pioneers the field of summation with the formula summing 1: n as ( n ( n + 1 ))/ 2, at the age of 7.
The discrete analog of curvature, corresponding to curvature being concentrated at a point and particularly useful for polyhedra, is the ( angular ) defect ; the analog for the Gauss – Bonnet theorem is Descartes ' theorem on total angular defect.
Carl Friedrich Gauss is credited with developing the fundamentals of the basis for least-squares analysis in 1795 at the age of eighteen.
This is the special case of Gauss – Bonnet, where the curvature is concentrated at discrete points ( the vertices ).
* Gauss – Bonnet Theorem at Wolfram Mathworld
Especially, Gauss had looked at the case of imaginary quadratic fields: he found exactly nine values of < math > D < 0 </ math > for which the ring of integers is a PID and conjectured that there are no further values.
The average magnetic field strength in the Earth's outer core was measured to be 25 Gauss, 50 times stronger than the magnetic field at the surface.
The average magnetic field in the Earth's outer core was calculated to be 25 Gauss, 50 times stronger than the field at the surface.
The regular heptadecagon is a constructible polygon ( that is, one that can be constructed using a compass and unmarked straightedge ), as was shown by Carl Friedrich Gauss in 1796 at the age of 19.
He studied mathematics and astronomy from 1811 at the University of Göttingen under Carl Friedrich Gauss ; but he enlisted in the Hanseatic Legion for the campaign of 1813 – 1814, and became lieutenant of artillery in the Prussian army in 1815.
As Germany provided little opportunity to study higher mathematics at the time, with only Gauss at the University of Göttingen who was nominally a professor of astronomy and anyway disliked teaching, Dirichlet decided to go to Paris in May 1822.

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