Contributions of mathematicians pdf 3

Contributions of mathematicians pdf 3

1. CONTRIBUTIONS OF MATHEMATICIANS

CARL FRIEDRICH GAUSS

2. CARL FRIEDRICH GAUSS

3. Carl Friedrich Gauss – in a short glance…
 Astronomer
 Physicist
 Mathematician
Amazing Gauss !!
 Three years old Gauss corrected a math error
his father has made.
 His primary school teacher is Buttner.
 Teacher gave a problem on Arithmetical
Progression:
81297 + 81495 + 81693 + …………… + 100899
 This Arithmetical Progression has common
difference, d = 198 and totally 100 terms,
n = 100.
 Gauss solved this problem using the formula,
S = ½ n(n + 1).
 He invented this formula at the age of 7 years.

4.  According to Laplace ,
“What to talk of Europe , Gauss is the greatest
mathematician of the world !”
BORN
 Original name - Johann Carl Friedrich Gauss
 Born on 23 April 1777
 Born at Brunswick , Germany
 Father - Gerhard Gauss (day labourer)
 Mother (illiterate)
 Mother remembers that Gauss born on a
Wednesday, eight days before the Feast of the
Ascension (which occurs 39 days after Easter).
 Gauss later solved this puzzle about his birth date
in the context of finding the date of Easter.

5. IN SCHOOL
• Gauss shows amazing attitudes towards figures.
• By 10 years , there is nothing to teach him in
arithmetic.
• Started to study Algebra and Geometry
• By 12 years, Gauss studied Binomial Theorem ,
Theory of infinite series and Possibility of non-
Euclidean Geometry.

IN COLLEGE
• Studied in the University of Gottingen
• At the University of Gottingen, Gauss met Kastner.
• Gauss and Kastner together continued discoveries
with theory of numbers.
• By 1796, Gauss choose Mathematics as his field.
• As C.F.Gauss says,
“Mathematics is the queen of science and
Arithmetic is the queen of all Mathematics.”

6. CAREER
• Gauss worked as a Math tutor from 1799.
• In 1801, he published first book named
‘Desquisitiones Arithmetica’.

• Then he joined in University of Helmstadt.
• There he met Johann .F. Pfaff and this friendship
continue till the end.
• He got Doctor’s degree in 1799.

7. • In 1807, Gauss appointed as Director of the new
Gottingen observatory and professor of
Mathematics of that University.
• In 1809,he published second master piece ‘Theoria
Motus’.
• In 1821, he published his third book ‘Superficious
Curvas’.
• At the age of 70, he added proof for his
fundamental theorems of Algebra.

FAMILY
• On 9 October 1805, Gauss married Johanna Osthoff,
and had a son and a daughter with her.
• Johanna died on 11 October 1809.
• Then he married Minna Waldeck on 4 August 1810,
and had three more children.
• Minna Waldeck died on 12 September 1831.

8. (Daughter Theresa)


DEATH
• Gauss was active until a few months before death.
• Died on February 23,1855.
• Died at the age of 77.

9. • Signature:



CONTRIBUTIONS
• At the age of 19 ,on March 30 1796 , Gauss
constructed a polygon of 17 sides with the help of a
ruler and compass only .
• In the first book ‘Desquisitiones Arithmetica’, we
can see the following :
1) Proofs of Algebraic statements
Every integral rational equation in
a single variable has at least one
root.

10.  Every equation will have as
many roots as the highest power
of the unknown .
2) Presented total picture of number system
(positive , negative, rational ,irrational,
imaginary )
• Uses the symbol
i = √ (-1)
• Uses the term ‘complex number ‘
• Made changes in the calendar system
• At the age of 24, predicted the orbits of newly
discovered planets.
• Researches in Differential Geometry, Theory of
surfaces, Statistics.

• In Probability, Gauss derived famous law “Gaussian
law of Normal Distribution of Errors “.

• He is the first to study what is known as non
Euclidean Geometry .

11. • Discovered the methods used in the branches of
Measurement of curvature , Theory of conformal
mapping and Applicability of Surfaces.

• In the field of Magnetism and Electricity .

• Probability of sending telegraphic signals with
scientists like Galvanic Volta and Ampere.


Conclusion
Carl Friedrich Gauss is considered as one of the
eminent Mathematicians of the world. He led the
Mathematical thinking in a new direction by the
discovery of complex numbers. He started an abstract
thinking in this field. That’s why Carl Friedrich Gauss is
known as ‘the prince of Mathematics’.