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ARCHIMEDES LAB PROJECT

Inspiring and Creative Resources & Tutorials for Science-Curious People

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POSTS

Posted on July 7, 2024


DISJUNCTIVE NUMBERS

Champernowne’s constant, denoted as 0.123456789101112… , is formed by
concatenating successive natural numbers. It can be represented as an infinite
series. Concatenating 0. with prime numbers yields the Copeland–Erdős constant.


Posted on July 5, 2024July 5, 2024


X LOG(Π) = Π LOG(X) ?

Are there other real solutions than x = π ?




show solutionhide solution


Solution: x = 2.38217908799…
Posted on May 13, 2024


JOURNEY OF A RING ALONG A PENROSE TRIANGLE

A neat animated tribar! It’s worth noting that the tribar, or Penrose triangle
(aka Reutersvärd triangle), attributed to British mathematician Roger Penrose,
was not technically ‘invented’ or ‘discovered’ by him. The geometric principles
underlying its existence were already evident in Greek and Arabic ornamentation,
including tiling and friezes…

Posted on April 10, 2024


NUMBERS DEFYING CEILING AND FLOOR FUNCTIONS

Two sequences that agree for an embarrassingly long time.



Read further…

Posted on March 25, 2024March 25, 2024


CIRCLES & ROOTS

Delve into the realm of Sacred Geometry, where circles unveil the elegance of
successive square roots from 1 to 6. Extend your exploration with the enigmatic
charm of the square root of Phi.



Picture available as prints and merchandise from our online gallery.

Posted on March 25, 2024


APPARENT SIZE ≠ REAL SIZE

Simple demonstration of apparent size and distance… See how the color rings
(annuli, in mathematical language) fit snugly.

Posted on March 12, 2024


THE ORIGIN OF MODERN ALPHABETS

The Phoenician alphabet is a writing system exclusively representing consonants,
requiring readers to infer vowel sounds. Beginning in the ninth century BC,
adaptations of this alphabet thrived, including Greek, Old Italic, and Anatolian
scripts. Its appealing feature was its phonetic nature, with each sound
(including vowels) represented by a single symbol, simplifying learning to only
a few dozen symbols.

The Phoenician alphabet is an abjad writing system.



Posted on March 3, 2024


NESTED PENROSE TRIANGLES

This is an illusory geometric structure that cannot exist in our 3D world.
Let’s Explore its captivating depths and intrigue.

Here’s how to create this impossible structure. Start by drawing two parallel
lines spaced apart from each other and divide them into 7 equally spaced lines.

Then follow the visual steps A, B, C, and D illustrated below. At the beginning
(fig. A), you will need to replicate the alignment of the 9 parallel lines three
times while applying a 60-degree rotation to each one, finally arranging them to
form a triangle. Subsequently, follow the visual directions in B and C to obtain
the figure shown in fig. D.

© Giannisarcone.com, source.

At last, you can add color and gradients to the structure as illustrated below.

© Giannisarcone.com, source.

Discover prints and merchandise featuring this op art masterpiece at my online
gallery. 

© Giannisarcone.com, source.



Posted on March 3, 2024


TOPOLOGICAL ODDITY: A PICTURE-HANGING PUZZLE

Imagine the linear pattern as a hanging rope. Now, removing any one of these
four nails will cause the entire rope to fall.

Image courtesy of Flickr user fdecomite.

Explore further…

Posted on February 27, 2024May 13, 2024


ILLUSORY STRUCTURES

That’s what happens when you fall down a Penrose staircase…


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ABOUT ARCHIMEDES LAB

Mental activities and tutorials that enhance critical and creative thinking
skills.

Our expertise lies in delivering engaging educational and entertaining content
to book and magazine publishers. In addition, we specialize in creating
innovative thinking games and visually appealing materials for various
applications, including recreation, culture, and advertising.


Buy us a coffee


CATEGORIES

Categories Select Category Animation Curiosity Equations Experiments Geometry
History Humor Kinetics Kynetics Language Magic Mathematics Nature New Release
Numbers Optical illusion Perception Puzzle Science Series Theorem Topology
Tridimensional Uncategorized


RECENT POSTS

 * Disjunctive Numbers July 7, 2024
 * x log(π) = π log(x) ? July 5, 2024
 * Journey of a Ring Along a Penrose Triangle May 13, 2024
 * Numbers Defying Ceiling and Floor Functions April 10, 2024
 * Circles & Roots March 25, 2024
 * Apparent size ≠ Real size March 25, 2024
 * The Origin of Modern Alphabets March 12, 2024


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July 2019 May 2019 April 2019 March 2019 January 2019 December 2018 November
2018 October 2018 September 2018 August 2018 May 2018 January 2018 December 2017


TAGS

 * 8 (2)
 * art (3)
 * circle (3)
 * circles (4)
 * cube (2)
 * cubes (3)
 * design (2)
 * dodecagon (2)
 * donut (2)
 * doughnut (2)
 * escher (3)
 * fibonacci (8)
 * fraction (2)
 * fractions (2)
 * gianni sarcone (4)
 * golden angle (2)
 * golden ratio (3)
 * hexagon (4)
 * illusion (2)
 * infinite (2)
 * Klein bottle (2)
 * knots (2)
 * Magic (4)
 * magic square (5)
 * numbers (4)
 * penrose (4)
 * pentagon (2)
 * phi (7)
 * Pi (9)
 * playing cards (2)
 * points (2)
 * prime (5)
 * prime number (2)
 * Puzzle (3)
 * right triangle (5)
 * Series (2)
 * spiral (2)
 * square (6)
 * square root (4)
 * squares (3)
 * sum of cubes (3)
 * theorem (7)
 * topology (5)
 * triangle (4)
 * two (2)


OUR RECENT EDUCATIONAL BOOKS

Eye Bogglers
ISBN 1780970749
Ultimate Eye Twisters
ISBN 1783124482


Fantastic Optical Illusions
ISBN 178739235X
Illusion d'Optique playing card deck


Optical Illusions
ISBN 1682973395
You can't possibly color this!
ISBN 1633223515


Impossible Folding Puzzles
ISBN 0486493512
Hidden Picture Puzzles
ISBN 1623540380


How To Draw Incredible Illusions
ISBN 1623540607
Amazing Optical Illusions
ISBN 1787391639




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contact@archimedes-lab.org


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