Image: Hopf Fibration. contrat Creative Commons France. Certains droits réservés.

Travel from 2D to 4D in 2 hours through 9 chapters:

Film Guide:

These lessons are suitable for Secondary-Elementary through University-level students, depending upon prior knowedge.
Commentary in Arabic, English, French, Spanish.
Subtitles in Arabic, Chinese, Dutch, English, French, German, Hebrew, Italian, Japanese, Portugese, Spanish, Russian.

Chapter 1: Dimension Two
Chapter 2: Dimension Three
Chapter 3: Dimension Four
Chapter 4: Dimension Four
Chapter 5: Complex Numbers
Chapter 6: Complex Numbers
Chapter 7: Fibration
Chapter 8: Fibration
Chapter 9: Proof

View online or order DVD.


« 4D Microscope Revolutionizes the Way We Look at Nano World »:

[For those of you soon entering Winter Recess: May your repose render at least one solitary, stupendous "EUREKA!" moment. May this posting help to foster such]. -LLP

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Tags: 2D, 3D, 4D, 4D_and_nano, Heinz_Hopf, Hopf_fibration, circles, circles_in_space, complex_numbers,, More…hypersphere, polytopes, spatial_dimensions, tori


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Welcome - about us

Welcome! Nanopaprika was cooked up by Hungarian chemistry PhD student in 2007. The main idea was to create something more personal than the other nano networks already on the Internet. Community is open to everyone from post-doctorial researchers and professors to students everywhere.

There is only one important assumption: you have to be interested in nano!

Nanopaprika is always looking for new partners, if you have any idea, contact me at

Dr. András Paszternák, founder of Nanopaprika

Publications by A. Paszternák:

Smartphone-Based Extension of the Curcumin/Cellophane pH Sensing Method

Pd/Ni Synergestic Activity for Hydrogen Oxidation Reaction in Alkaline Conditions

The potential use of cellophane test strips for the quick determination of food colours

pH and CO2 Sensing by Curcumin-Coloured Cellophane Test Strip

Polymeric Honeycombs Decorated by Nickel Nanoparticles

Directed Deposition of Nickel Nanoparticles Using Self-Assembled Organic Template,

Organometallic deposition of ultrasmooth nanoscale Ni film,

Zigzag-shaped nickel nanowires via organometallic template-free route

Surface analytical characterization of passive iron surface modified by alkyl-phosphonic acid layers

Atomic Force Microscopy Studies of Alkyl-Phosphonate SAMs on Mica

Amorphous iron formation due to low energy heavy ion implantation in evaporated 57Fe thin films

Surface modification of passive iron by alkylphosphonic acid layers

Formation and structure of alkylphosphonic acid layers on passive iron

Structure of the nonionic surfactant triethoxy monooctylether C8E3 adsorbed at the free water surface, as seen from surface tension measurements and Monte Carlo simulations

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