1 / 11

Johann Carl Friedrich Gauss

Johann Carl Friedrich Gauss. 1777 – 1855 Germany. Johann Carl Friedrich Gauss. Geodesy Geophysics Electrostatics Astronomy Optics. Number Theory Algebra Statistics Analysis Differential Geometry. 1777 – 1855 Germany. Disquisitiones Arithmeticae -1801.

Download Presentation

Johann Carl Friedrich Gauss

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Johann Carl Friedrich Gauss 1777 – 1855 Germany

  2. Johann Carl Friedrich Gauss • Geodesy • Geophysics • Electrostatics • Astronomy • Optics • Number Theory • Algebra • Statistics • Analysis • Differential Geometry 1777 – 1855 Germany

  3. Disquisitiones Arithmeticae -1801

  4. Disquisitiones Arithmeticae -1801 • Division of a circle of polygon was dependant on Higher Arithmetic. • 17-Gon Construction with compass and ruler

  5. Disquisitiones Arithmeticae -1801 • Division of a circle of polygon was dependant on Higher Arithmetic. • 17-Gon Construction with compass and ruler • Systematic Introduction to Modular Arithmetic • Similar to how Euclid broke down the Elements

  6. Disquisitiones Arithmeticae -1801 • Fundamental Theorem of Algebra • Every Non-Constant Single Variable Polynomial with Complex Coefficients had as least one Complex Root

  7. Disquisitiones Arithmeticae -1801 • Fundamental Theorem of Algebra • Every Non-Constant Single Variable Polynomial with Complex Coefficients had as least one Complex Root • Quadratic Reciprocity • If p = 1 (mod4) or q = 1 (mod4) then p/q = q/p • If p,q = 3 (mod4) then p/q = -p/q

  8. 17-Gon

  9. 17-Gon PREREQUISITES: • Euclidean Geometric Constructions • Doubling sides technique.

  10. 17-Gon PREREQUISITES: • Euclidean Geometric Constructions • Doubling sides technique. • Imaginary Plane – Caspar Wessel • z = x + iy • z = r (cos θ + i sin θ)

  11. 17-Gon PREREQUISITES: • Euclidean Geometric Constructions • Doubling sides technique. • Imaginary Plane – Caspar Wessel • z = x + iy • z = r (cos θ + i sin θ) • Vertices of the n-gon is a root of unity. • An nth root of unity is any complex number s.t. z^n = 1 • (Primitive root if no other roots z^k = 1 exist where k < n)

More Related