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Ambigram Magic Squares

When using standard characters, the digits 0, 1, and 8 are symmetrical around the horizontal axis, while 6 and 9 are interchangeable when rotated 180 degrees.

With these digits, we can create magic squares that maintain their constant sum even when flipped, as illustrated below.

Interestingly, when these numbers are represented in LCD style, we can also include the digit 2, which resembles a 5 when inverted. This allows for the creation of magic squares with additional properties related to both 2D and 3D symmetry—whether flipped or mirrored—such as the remarkable example created by Chris Wardle.

This isn’t the first magic square to exhibit such fascinating properties; there are many variations out there. I encourage you to explore and discover your own creations online. If you have original ideas for magic squares with these unique characteristics, we would love for you to share them with us!

For those interested in learning more about the history and mathematics behind magic squares, check out this fascinating article from the Royal Institution: The Fascination of Magic Squares.

More links of interest:
[1] https://www.rigb.org/explore-science/explore/blog/fascination-magic-squares
[2] https://math.hmc.edu/funfacts/magic-squares-indeed/
[3] https://patcherymenagerie.blogspot.com/2019/07/magic-squares.html
[4] https://www.geeksforgeeks.org/magic-squares-fun-fact-and-more/
[5] https://mathcommunities.org/magic-squares/
[6] https://www.magischvierkant.com/links-eng/
[7] https://chelekmaths.com/2020/06/30/cracking-the-cryptic-joy-and-magic-squares/
[8] https://www.byrdseed.tv/magic-squares/

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Cylindrical Anamorphosis of Hand With Reflecting Sphere

M.C. Escher’s 1935 lithograph Hand With Reflecting Sphere inspired artist Kelly M. Houle to create her own interpretation in charcoal on illustration board. When a cylindrical mirror is placed at the center, it produces a striking reflection. Houle explains, “When the original image is bent and stretched into a circular swath, the shadows seem to fall in all directions. When the curved mirror is used to reflect the anamorphic distortion, the forms take on the familiar rules of light and shading, making them appear three-dimensional” (Kelly M. Houle, “Portrait of Escher: Behind the Mirror,” in D. Schattschneider and M. Emmer, eds., M.C. Escher’s Legacy, 2003).

The original work.
Circular anamorphosis of the original work as seen by an observer.
Final result: 3D cylindrical anamorphosis.

Cylindrical anamorphosis is an art technique that creates distorted images that appear normal when viewed through a cylindrical mirror, manipulating perspective and light to produce a three-dimensional effect from a two-dimensional surface.

About Kelly M. Houle

Kelly M. Houle is known for her work in anamorphic art and illuminated manuscripts. Her projects often blend artistic expression with scientific themes, such as her illuminated manuscript based on Darwin’s On the Origin of Species. She has exhibited her work widely and continues to explore innovative techniques in contemporary art.

For more information about her work, visit Kelly M. Houle’s website.

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Invisible Artworks: The Absurdity of Nothingness in Contemporary Art?

In the world of contemporary art, the concept of invisibility has become an imaginative playground for creativity. Here’s a glimpse into some intriguing—and often humorous or haunting—examples of invisible artworks that challenge our perceptions and redefine what art can be.

Notable Invisible Artworks:

1. Yves Klein – ‘Zone de Sensibilité Picturale Immatérielle’ (1959)

   Klein sold ownership of empty space, allowing collectors to own nothingness itself. A bold move that encourages us to consider the value of absence!

2. Marinus Boezem – ‘Show V: Immateriële ruimte’ (1965)

    This piece features “air doors” made of cold and warm air currents, inviting viewers to experience immateriality.

3. Michael Asher – ‘Vertical Column of Accelerated Air’ (1966) 

    Asher composed a work entirely of drafts of pressurized air, encouraging participants to engage through sensation rather than sight.

4. Art & Language – ‘Air-Conditioning Show’ (1967)

   This installation featured an empty room with two air conditioning units, emphasizing that the true art lies in the feelings and conversations it inspires. Talk about a cool concept!

5. James Lee Byars – ‘The Ghost of James Lee Byars’ (1969)

   Byars designed a pitch-black room, inviting visitors to contemplate emptiness. It’s like stepping into a fridge at midnight—dark and full of existential questions.

Continue reading “Invisible Artworks: The Absurdity of Nothingness in Contemporary Art?”
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A Remarkable Op’ Artwork Selected by NASA: ‘Moona Lisa’

Today, September 14th, we are thrilled to announce that Gianni Sarcone‘s op’ artwork “The Moona Lisa” has been selected as NASA’s Astronomy Picture of the Day for the International Observe the Moon Night. This captivating piece, created in collaboration with astrophotographer Marcella Giulia Pace, showcases a stunning arrangement of lunar images that, when viewed from a distance, reveal the iconic portrait of the Mona Lisa by Leonardo da Vinci.

Image Credit & Copyright: Gianni Sarcone and Marcella Giulia Pace

The vibrant colors of the moons are naturally derived from atmospheric conditions and sunlight reflections at various times, creating a unique visual experience. “The Moona Lisa” not only pays homage to da Vinci’s genius but also highlights the remarkable capacity of our brains to recognize faces, even when obscured.

Image Credit & Copyright: Gianni Sarcone and Marcella Giulia Pace

You can explore the full image and learn more about it on NASA’s website.

Additionally, prints of this op artwork are available for purchase in our online gallery. It’s a unique opportunity to own a piece that celebrates the Moon and reinterprets a Leonardo-inspired icon through a captivating visual illusion.

Join us in celebrating this fusion of art and science, and experience the magic of “The Moona Lisa.”

This GIF illustrates the creation process of Moona Lisa. For more details, visit Sarcone’s Behance page.

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Exploring Impossible Figures: A Philosophical Twist on Reality

Impossible figures are intriguing forms that defy the reality of our 3D world. In the 90s, I began experimenting with representations of cylinders featuring fictitious right angles—an artistic play on geometry. These twisting impossible figures, which defy mathematics and physics, are ideal for interior decoration or merchandise like t-shirts or mugs because they captivate the viewer’s imagination and provoke thought. Their striking, paradoxical nature draws attention, making them perfect conversation pieces, while also offering a philosophical twist on the idea that what seems real may not always be.

By stripping those imaginary geometric form down to their essence, I instill them with greater power.

These drawings are taken from my book Drawing Optical Illusions, still available on Amazon.

And are available as prints and t-shirts and merch from my online gallery!

Buy prints and apparels here: https://redbubble.com/shop/ap/164384901
Buy prints and apparels here: https://redbubble.com/shop/ap/164477598
Buy prints and apparels here: https://redbubble.com/shop/ap/164403619
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Numeronyms in Chinese

Numeronyms, a fascinating aspect of Chinese internet slang, utilize numbers to represent phrases or concepts based on their phonetic similarities. This shorthand is commonly used in online communication, allowing users to convey messages succinctly and creatively. Below are some popular Chinese numeronyms and their meanings:

  • 007 – Represents a work schedule of 00:00 hours to 00:00 hours, 7 days a week (pinyin: línglíngqī), a variant of the 996 working hour system.
  • 1314 – Means “forever,” often used in romantic contexts, as in “I love you forever.” It corresponds to 一生一世 (pinyin: yīshēng yīshì).
  • 213 – Refers to “2B,” which is a derogatory term for someone perceived as very stupid (二逼).
  • 233 – Represents laughter, equivalent to 哈哈哈 (pinyin: hāhāhā).
  • 250 – Means “stupid,” derived from historical currency references (pinyin: èrbǎiwǔ).
  • 38 – Refers to a woman who gossips excessively.
  • 4242 – Indicates “yes” or “affirmative,” representing 是啊是啊 (pinyin: shìa shìa).
  • 484 – Stands for “if,” corresponding to 是不是 (pinyin: shìbùshì).
  • 520 – Means “I love you,” as it sounds similar to 我爱你 (pinyin: wǒ ài nǐ).
  • 555 – Represents crying, mimicking the sound 呜呜呜 (pinyin: wūwūwū).
  • 666 – Indicates something “cool” or “nice,” derived from gaming slang where it signifies impressive skill (pinyin: liùliùliù).
  • 777 – A variation of 666, meaning “even better.”
  • 7451/7456 – Expresses anger, translating to 气死我了 (pinyin: qìsǐwǒle), meaning “I’m furious.”
  • 748 – An aggressive phrase meaning “Go and die!” (去死吧, pinyin: qùsǐba).
  • 87 – Refers to being “bitchy” or “idiotic” (白痴, pinyin: báichī).
  • 88 – A casual way to say “bye bye” (拜拜, pinyin: bābā).
  • 94 – Functions as a conjunction, meaning “so” or “but” (就是, pinyin: jiùshì).
  • 955 – Represents a typical 9 to 5 job (pinyin: jiǔwǔwǔ).
  • 99 – Symbolizes the wish for a couple to be together for a long time (久久, pinyin: jiǔjiǔ).
  • 995 – A plea for help, meaning “Save me!” (救救我, pinyin: jiùjiùwǒ).
  • 996 – Refers to the demanding 996 working hour system (pinyin: jiǔjiǔliù).
  • 999 – Similar in meaning to “666,” often used to express approval.

These numeronyms reflect the creativity and efficiency of language use in the digital age, showcasing how numbers can convey complex emotions and ideas in a concise manner.

⇨ Further reading.

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The Doppler Effect: A Mathematical Symphony

Imagine a siren on a fire truck…
· When the truck is approaching you: The siren’s sound waves are compressed, making it sound higher pitched. It’s like the truck is “pushing” the waves together.
· When the truck is moving away from you: The siren’s sound waves are stretched out, making it sound lower pitched. It’s like the truck is “pulling” the waves apart.
This is the Doppler effect: the change in pitch of a sound wave due to the relative motion between the source of the sound and the observer.
The same concept applies to light waves, with objects moving toward us appearing bluer and those moving away appearing redder.

⇨ Further reading.

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Impossible Escape: A Topological Illusion

This is a fun and surprising escape trick for kids and family, that uses simple props:

· 1 karabiner clip,

· 1 metal ring,

· 1 loop of cord.

To begin:

1. The ring and the green karabiner clip are securely attached to the cord and cannot be removed.

2. Now, watch closely as I attach the green karabiner to the metal ring, making the setup even more complex.

3. Surprisingly, I can now simply pull the cord free.

Can you believe your eyes? Let’s try it together!

More topological magic tricks:

– https://archimedes-lab.org/2021/06/29/magic-topology-2/

– https://archimedes-lab.org/2020/06/09/magic-topology/

– https://archimedes-lab.org/2017/12/14/how-to-magically-untie-a-shoelace-double-knot/

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When Intuition Fails: Borwein Integrals

Borwein integrals, introduced by David and Jonathan Borwein in 2001, are a classic example of how intuition can be misleading in mathematics. Defined using the sinc function (sin(x)/x), these integrals initially appear to consistently equal π/2. However, this pattern unexpectedly breaks down when the factor sinc(x/15) is introduced, surprising even experienced mathematicians. This phenomenon underscores the importance of rigorous proof over reliance on patterns.


Read further. 


[David Borwein and Jonathan M. Borwein, “Some Remarkable Properties of Sinc and Related Integrals,” Ramanujan Journal 5:1 (March 2001)]