From diffgeom.com
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Building love of math: original, distinctive, high-quality mathematical images and objects designed to arouse curiosity and wonder, to cultivate appreciation for the beauty of geometry, analysis, and algebra, to build mathematical understanding
on Tue, 6PM
From diffgeom.com
Winter Light Greeting Cards Box of 10
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A pack of 10 greeting cards with envelopes. Blank inside. Printed in the UK on 330gsm Fedrigoni card stock, assembled in the US.
on Oct 22
From diffgeom.com
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At Differential Geometry, original designs celebrate the grace of form. All earrings are assembled using sterling silver ear wires and jump rings, and come ready to wear. For customers outside the US: Please note that your country may assess an import duty, which must be paid separately for your...
on Oct 20
From diffgeom.com
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At Differential Geometry, new jewelry designs undergo successive phases of development. Sometimes, at the end of this process, a production-ready piece is not selected to become part of the regular catalog. These limited-edition wearables (almost all of them one-of-a-kind) are listed here....
on Oct 20
From diffgeom.com
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Crescendo, a doubly-covered Möbius strip, suggests an ever-breaking wave. This elegant 1-1/4 in (32mm) pendant is 3D printed in sterling silver, polished to a mirror-like luster, and paired with an 18-inch sterling silver rope chain with lobster claw clasp.
on Oct 7
From diffgeom.com
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Crescendo, a doubly-covered Möbius strip, suggests an ever-breaking wave. This elegant 1-1/4 in (32mm) pendant is 3D printed in gold-plated sterling silver, polished to a mirror-like luster, and paired with an 18-inch 14K gold-filled loop chain with spring clasp.
on Oct 7
From diffgeom.com
Square roots with a complex twist
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In this post we'll build a bridge starting with the parabola familiar from plane geometry and arriving at the "Riemann surface of the complex square root," which often mystifies complex analysis students.
on Aug 28
From diffgeom.com
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Symmetry Natural forms such as snowflakes, sea shells, water droplets, mineral crystals, and faces exhibit "symmetry." Often, symmetry correlates with beauty: a visual stimulus translated directly to sensations of pleasantness without words or conscious thought. In this post we'll explore what...
on Aug 7
From diffgeom.com
Morse Theory, Oblique Unisex Short Sleeve T-Shirt
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Crew neck T-shirt with short sleeves and designed with superior Airlume combed and ring-spun cotton. Offered in a variety of solid and heather cvc colours.
on Jul 28
From diffgeom.com
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Our Anemone collection depicts torus knots, curves or bands that wind along the surface of a mathematical donut.This one-of-a-kind 1-3/8 in (35mm) brooch pin prototype is 3D printed in 18K gold-plated brass, polished to a mirror-like luster, and mounted on a 1/2-in (13mm) silver-plated steel pin...
on Jul 14
From diffgeom.com
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Our Anemone collection depicts torus knots, curves or bands that wind along the surface of a mathematical donut.This one-of-a-kind 1-3/8 in (35mm) brooch pin prototype is 3D printed in rose gold-plated brass, polished to a mirror-like luster, and mounted on a 1/2-in (13mm) silver-plated steel...
on Jul 14
From diffgeom.com
Double Slit Experiment Wall Art Poster
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When a wave passes through a barrier with a hole of diameter comparable to the wavelength, the hole acts approximately like a point source. If the barrier contains two holes, the waves from the point sources may interfere, having high amplitude (dense dots) where crests align with crests and...
on Jul 10
From diffgeom.com
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The mathematics of stereographic projection retrieves this banded torus from the unit sphere in four-space. The bands' edges are unit circles, any two linked. The torus itself is gently tilted in four-space, giving its solid shadow in three-space an enticing asymmetry. This eye-catching 1 in...
on Jun 26
From diffgeom.com
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The mathematics of stereographic projection retrieves this banded torus from the unit sphere in four-space. The bands' edges are unit circles, any two linked. The torus itself is gently tilted in four-space, giving its solid shadow in three-space an enticing asymmetry. This eye-catching 1 inch...
on Jun 26
From diffgeom.com
Nowhere Differentiable, Sky Mug
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Printed on a sturdy cylindrical 12 oz. (350 mL) white ceramic mug with handle. Microwave and dishwasher safe.
on Jun 25
From diffgeom.com
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A knot suggesting linked rings, choreography, and harmony. The mathematics of stereographic projection retrieves this evocative symbol from a Clifford torus knot on the unit sphere in four-space. This distinctive 1-3/8 in (35mm) pendant is 3D printed in rhodium-plated brass, polished to a...
on Jun 24
From diffgeom.com
Monuments, Desert Wall Art Poster
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The imaginary part of the complex exponential function, \(z = e^{x} \sin y\), oscillates in \(y\) and grows exponentially in \(x\). When we stand on the \((x, y)\)-plane to the left of the origin and look rightward through fog, the oscillations loom before us like an infinite procession of...
on Jun 23
From diffgeom.com
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Soap films present delicately-varying saddle shapes. Agile (ah Zheel, the musical term) represents a ring-shaped region on Enneper's surface with five-fold symmetry.This dramatic 1-1/4 in (30mm) pendant is 3D printed in 18K gold-plated brass, polished to a mirror-like luster, and paired with an...
on Jun 2
From diffgeom.com
Idea: Contemplation Wall Art Poster
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Inspiration has struck: The initial flash has faded to a glow, but the shape remains definite. A sphere with icosahedral symmetry inspired by temari balls floats in a twilight sky above a range of virtual mountains. The second part of a triptych with "Inspiration" and "Dreaming." Printed on...
on May 30
From diffgeom.com
Idea: Inspiration Wall Art Poster
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The moment inspiration strikes: A luminous, fireworks-like sphere, with icosahedral symmetry inspired by temari balls, blooms in a sunset sky above a range of virtual mountains. The first part of a triptych with "Contemplation" and "Dreaming." Printed on high-quality 170 gsm poster paper with a...
on May 30
From diffgeom.com
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The idea, cooled and tempered, enters the mind's liminal spaces, ready to help catalyse further inspiration. A shadowed sphere with icosahedral symmetry inspired by temari balls floats in a nighttime sky above a range of virtual mountains. The third part of a triptych with "Inspiration" and...
on May 30
From diffgeom.com
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Intimo suggests two interlinked rings, but on closer gaze is revealed to be a single entwined union whose shape varies intriguingly. The mathematics of stereographic projection retrieves this distinctive symbol of lasting love from a Clifford torus knot on the unit sphere in four-space. These...
on May 29
From diffgeom.com
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Soap films present elegant saddle shapes. The catenoid, a surface of rotation, and the helicoid, a ruled surface made entirely of lines, have been known to mathematicians since the 18th century. The catenoid and helicoid are united in a one-parameter family of soap films. Our lively, ascending...
on May 22
From diffgeom.com
Lotus Sunset, Scape Wall Art Poster
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An invertible, complex-differentiable mapping from the open disk to the disk with the vertical radial ray removed sends a polar coordinate grid to the lotus-like grid shown. This coordinate grid floats above a range of virtual mountains whose nearest range is a sine graph, whose successive...
on May 21
From diffgeom.com
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The mathematics of stereographic projection retrieves this banded torus from the unit sphere in four-space. The bands' edges are unit circles, any two linked. The torus itself is gently tilted in four-space, giving its solid shadow in three-space an enticing asymmetry. This luminous 1-3/8 in...
on May 14
From diffgeom.com
0 0
The mathematics of stereographic projection retrieves this banded torus from the unit sphere in four-space. The bands' edges are unit circles, any two linked. The torus itself is gently tilted in four-space, giving its solid shadow in three-space an enticing asymmetry. This luminous 1-3/8 in...
on May 14
From diffgeom.com
Luminography, Forge Wall Art Poster
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Mathematical objects exist only as abstractions in the mind. When one's life is devoted to mathematics, however, mathematical objects can come to seem not merely real, but ubiquitous, and larger than life. The electric fireworks in this evening sky are a model of the real projective plane, a...
on May 9
From diffgeom.com
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At the Differential Geometry math art shop, our unique jewelry celebrates the grace of form. Elegant for special occasions, practical for daily wear.
on Apr 29
From diffgeom.com
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Rays and Perspective Imagine a flat floor extending to infinity in all directions and covered with square tiles, creating a Cartesian coordinate system. A parabola, such as the graph \(y = x^{2}\), is painted on the floor. If we stand below the origin and look at the parabola in perspective,...
on Apr 21
From diffgeom.com
Beautiful, Original Mathematical Ceramic Mugs: DiffGeom math art shop
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Our original mathematical images lend contemplative beauty and distinctive sophistication to your office or home, and invite pleasant conversation with friends and strangers alike! Designed by a professional mathematician, available exclusively from the Differential Geometry math art shop.
on Apr 19
From diffgeom.com
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At the Differential Geometry math art shop, our unique jewelry celebrates the grace of form. Elegant for special occasions, practical for daily wear. Pendants come paired with a chain as described and shown, and are ready-to-wear. Please email for information about purchasing pendants without chains.
on Mar 23
From diffgeom.com
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The mathematics of stereographic projection retrieves these banded tori from the unit sphere in four-space. The bands' edges are images of great circles, any two linked. The tori themselves are gently tilted in four-space, giving their solid shadows in three-space an enticing asymmetry. These...
on Mar 15
From diffgeom.com
0 0
Soap films present elegant saddle shapes. The catenoid, a surface of rotation, and the helicoid, a ruled surface made entirely of lines, have been known to mathematicians since the 18th century. The catenoid and helicoid are united in a one-parameter family of soap film surfaces. Our lively,...
on Mar 13
From diffgeom.com
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In this post we'll meet a staple at the Differential Geometry math art shop: Flat tori in four-space, and "conformal torus knots" lying on these surfaces. Although we generally strive in these posts to avoid coordinates, we'll refer to Cartesian coordinates throughout. Our story starts with...
on Feb 29
From diffgeom.com
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A knot suggesting linked rings, choreography, and harmony. The mathematics of stereographic projection retrieves this evocative symbol from a Clifford torus knot on the unit sphere in four-space. This distinctive 35mm pendant is 3D printed in 18K gold-plated brass, polished to a mirror-like...
on Feb 21
From diffgeom.com
Nowhere-Differentiable, Desert Greeting Card
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Printed on high-quality 330gsm Fedrigoni card stock.
on Feb 12
From diffgeom.com
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The mathematics of stereographic projection retrieves these banded tori from the unit sphere in four-space. The bands' edges are images of great circles, any two linked. The tori themselves are gently tilted in four-space, giving their solid shadows in three-space an enticing asymmetry. These...
on Jan 19
From diffgeom.com
Area of Spherical Triangles Wall Art Poster
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In spherical geometry, a "triangle" has arcs of great circles as sides. The total interior angle of a spherical triangle exceeds \(\pi\) by an amount proportional to the triangle's area. On a sphere of radius \(R\), the constant of proportionality is \(1/R^2\), the "Gaussian curvature" of the...
on Dec 28
From diffgeom.com
Rational Fire, Warm Wall Art Poster
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A "rational number" is a fraction, a ratio of whole numbers. In the sense that integer arithmetic is exact, rational arithmetic is also exact. (By contrast, evaluating rational numbers in floating point form entails round-off error.) In a first real analysis course, students learn that every...
on Dec 23
From diffgeom.com
Ellipsoid Geodesics, Warm Wall Art Poster
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A geodesic on a surface generalizes a straight line in Euclidean geometry: For sufficiently-nearby points on a surface, a geodesic joining them is the shortest path between them and lying in the surface. Unlike in Euclidean geometry, a geodesic generally "winds around" on a surface, and is not...
on Dec 16
From diffgeom.com
Parabolic Ascent Wall Art Poster
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Plot a parabola on a sheet graph paper extending to infinity. If we stand on the vertical axis below the origin and look at the graph, what curve do we see? Perhaps surprisingly, we see an ellipse tangent to the horizon. If we position ourselves just right, we see a perfect circle. Printed on...
on Dec 13
From diffgeom.com
Line With Two Origins Wall Art Poster
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The line with two origins refers to the topological space obtained from two number lines by "gluing" each point of one line—except for the origin—to the corresponding point in the other line. Each point of the line with two origins has a neighborhood that looks just like an ordinary open...
on Dec 12
From diffgeom.com
Past and Future Wall Art Poster
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A right circular cone and hyperboloids of one and two sheets drawn pointilistically, in a metaphorically quantum way. These surfaces illustrate how a tube can "pinch off" to two disks in three-dimensional Morse theory. They also illustrate the geometry of special relativity, with the horizontal...
on Dec 10
From diffgeom.com
Five Tetrahedra, Winter Wall Art Poster
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Let \(\phi = \frac{1}{2}(1 + \sqrt{5})\) be the golden ratio. Start with a cube aligned with the Cartesian axes. Inscribe a regular tetrahedron whose vertices are alternate vertices of the cube. Rotate this tetrahedron by multiples of one-fifth of a turn about the axis through \((0, 1, \phi)\)...
on Dec 9
From diffgeom.com
Imagination, Forge Wall Art Poster
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Mathematical objects exist only as abstractions in the mind. When one's life is devoted to mathematics, however, mathematical objects can come to seem not merely real, but ubiquitous, and larger than life. The electric fireworks in this evening sky are a model of the real projective plane, a...
on Dec 7
From diffgeom.com
Nowhere-Differentiable, Desert Mug
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Calculus instructors often use the phrase ``continuous function'' (loosely, one whose graph has no jumps) while drawing a differentiable function (one whose graph has a tangent line at each point). It can therefore come as a conceptual shock to learn in real analysis that a continuous function...
on Dec 6
From diffgeom.com
0 0
Building love of math: original, distinctive, high-quality mathematical images and objects designed to arouse curiosity and wonder, to cultivate appreciation for the beauty of geometry, analysis, and algebra, to build mathematical understanding
on Dec 5
From diffgeom.com
Lotus, Sunrise Wall Art Poster
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A non-empty open set in the plane is "simply-connected" if any two points of the set are joined by a path lying in the set, and if every closed path in the set can be "shrunk to a point" staying within the set. Qualitatively, the set is in one piece, and does not enclose any holes. A disk, a...
on Dec 4
From diffgeom.com
Topological Index Wall Art Poster
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A vector field in the plane is a continuous assignment of a vector to each point in some plane region. To a topologist, a vector field that is nowhere zero in some disk "looks like" a constant non-zero field. If a vector field is zero at one point of a disk, there is an integer invariant, called...
on Nov 28