Name: Euclid's puzzling...
Uploaded: 2025-11-11T10:37:53.634Z
Description: Flat surfaces behave one way, while positively and negatively curved surfaces display very different characteristics. At first these alternative geometries seemed strange, but were soon found to be equally adept at describing the world around us. Navigating our planet requires elliptical geometry while the much of the art of M.C. Escher displays hyperbolic geometry.

Christopher Alexander

I believe that all centers that appear in space - whether they originate in biology, in physical forces, in pure geometry, in color - are alike simply in that they all animate space. It is this animated space that has its functional effect upon the world, that determines the way things work, that governs the presence of harmony and life.

American Architect

Julie Plec

I've learned that I've just barely scratched the surface of knowledge of the profession, and I have deep envy of and appreciation for filmmakers who really, truly understand the physics, the design of filmmaking. They can do story and color and composition and geometry and math and science all at once.

American Producer

Eve Arnold

If the chemistry is right between star and photographer and the geometry of the pictures pleases the star, often the two people end up with a long-term professional friendship during which they continue to work together and to produce highly personal images.

American Photographer

Richard P. Feynman

Einstein's gravitational theory, which is said to be the greatest single achievement of theoretical physics, resulted in beautiful relations connecting gravitational phenomena with the geometry of space; this was an exciting idea.

American Physicist

Sanjay Leela Bhansali

Some of the most beautiful people, to me, are those with the wrong geometry. Mother Teresa is extremely beautiful and not because she is a saint. Her characteristics are very strange, and that is what generates the power she had.

Indian Director

David Grinspoon

One of the weird things about modern physics is that we do find there are apparently these other dimensions that we don't directly experience that explain some aspects of the overall geometry and reality of our universe.

American Scientist

William Adams

Now being in such grace and favor by reason I learned him some points of geometry and understanding of the art of mathematics with other things, I pleased him so that what I said he would not contrary.

English Explorer

Priyamvada Natarajan

We already have a pretty good knowledge of the universe's mass-energy content, so if we can get a handle on its geometry, then we will be able to work out exactly what the fate of the universe will be.

Indian Scientist

Antony Garrett Lisi

I think the universe is pure geometry - basically, a beautiful shape twisting around and dancing over space-time.

Erno Rubik

I've always been passionate about geometry and the study of three-dimensional forms.

Hungarian Inventor

Geometry is used in academic settings and relates to studies involving space, shapes, and sizes.

Academic Subject

Understanding geometry helps develop problem-solving and logical reasoning skills, important in math.

Mathematical Reasoning

Geometry is not just for classrooms; it's used in art, architecture, engineering, and more.

Everyday Application

Geometry often describes the physical design and structure of everyday objects.

Physical Structures

Geometry in general context helps people understand and describe how spaces and objects are arranged.

Spatial Understanding

In computing, geometry is used to understand and create virtual models and environments.

Technical Use

Geometry plays a crucial role in graphic design, animation, and visual effects.

Visual Media

Understanding geometry helps in developing interactive apps or games that simulate real-world physics.

Interactive Environment

 Flat surfaces behave one way, while positively and negatively curved surfaces display very different characteristics. At first these alternative geometries seemed strange, but were soon found to be equally adept at describing the world around us. Navigating our planet requires elliptical geometry while the much of the art of M.C. Escher displays hyperbolic geometry.

Euclid's puzzling...

 So, ignoring the geometry lesson, and taking matters into their own hands, the bees went back to the drawing board to rethink their beehive design. One suggested triangles, "We can use triangles. Look! They fit together perfectly." Another bee suggested squares. Finally, a third bee piped up and said,

Why do honeybees love...

 were preserved and further developed, resulting in fundamental advancements in scientific study and mathematics. Accompanying this was an increasingly sophisticated use of abstraction and complex geometry in Islamic art, from intricate floral motifs adorning carpets and textiles,

The complex geometry of...

 Where is it? Well, to explain that, it's important to understand that artists and designers think in terms of shape and images but computers think in terms of numbers and equations. So, to bridge those two worlds we use a mathematical concept called coordinate geometry, right?

Pixar: The math behind...

 Carl wrote to Euler for help with the problem. Euler first dismissed the question as having nothing to do with math. But the more he wrestled with it, the more it seemed there might be something there after all. The answer he came up with had to do with a type of geometry

How the Königsberg...

 divided among the four branches of arithmetic, geometry, astronomy and music. These subjects were not studied merely for the sake of curiosity or practical utility, but because they authenticated the belief that numbers were the sacred language of the universe.

The murder of ancient...

 geometry they seek themself or even avoid themselves once I less trajectories onto the geometry we can actually add all sorts of information old connections thickness and bring back to the world of geometry why would we bring back to the world of geometry

Experiencing art as...

 it's the height of the room. Like I say, it's all that kind of three-dimensional surface geometry all around me. Well, Daniel, you have done a spectacular job of helping us all see the world in a different way. Thanks so much for that, truly. Thank you.

Daniel Kish: How I use...

 and source of all creation. Numbers were active agents in nature. Plato argued mathematical concepts were concrete and as real as the universe itself, regardless of our knowledge of them. Euclid, the father of geometry, believed nature itself

Is math discovered or...

 think we all know have a life in this photograph on the left there are the strong horizontal lines that define the graphics and design geometry of my childhood landscape another reason why it's fitting that it beyond the title

Geometry

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