http://www.dansmath.com/gallery daily 0.75 2025-06-30 https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1443307052398-3VYDBYWZTXKTW87TKPW2/dansmath14.jpg gallery - dan and the giant sphere at a small hideaway in sonoma, california lives a metal sphere apparently about 7 feet in diameter, and hence about 22 feet around. that's an interesting pattern on the surface. any guess as to how many little shapes cover the sphere? my hand fits through one of them. is it a polyhedron? https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1443307052398-3VYDBYWZTXKTW87TKPW2/dansmath14.jpg gallery - dan and the giant sphere at a small hideaway in sonoma, california lives a metal sphere apparently about 7 feet in diameter, and hence about 22 feet around. that's an interesting pattern on the surface. any guess as to how many little shapes cover the sphere? my hand fits through one of them. is it a polyhedron? https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1640282796329-Y78HUQOPER0B38X84CZS/Saddle+Firebird+1500.jpg gallery - saddle firebird the basic saddle (x, y, z) = (cos(t), sin(t), cos(2t)) is adorned with hundreds of sine waves based on the tangent, normal, and binormal vectors. trig functions attached to the {T, N, B} frame tell the story here. https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1476893836411-K31CNO2NCLEZYSBVO48D/3D+star+1.png gallery - dansmath logo (3D star - top view) starting with the outer red curve (a slightly wiggly circle), the curves change color as they march inward toward the center of curvature at each point. the slight wobble is magnified, especially vertically, as the curves go from orange to blue-green. this object has become my go-to lo-go. https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1477427425564-QABFCO3TCFCAV27KILQP/Balls+in+a+basket+small+sq.png gallery - spheres in a wire basket i dreamed up a twisty central curve and made mathematica draw the curves around it, with weird combinations of the T, N, B vectors doing the job. the spheres are sized to just touch the wires. https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1640282796255-4LW650FACE7HM5KUYV2O/Many+fewer+circles+half+rings+900.jpg gallery - circles in space there are lots of circles in this picture, but NONE OF THEM touch any others! based on a 1983 article I rescued from an old pile of AmerMathMonthly, I told Mathematica to put circles on each spherical shell that avoid the intersection with the vertical red rings. https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1551556720003-74PKA1VCOZEV3W5D2HNT/demi-3.png gallery - demiregular tiling made in girih.app - this tiling of triangles, squares, and hexagons can be extended to fill the whole plane. https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1476893643145-24KDVI6UBB6WN3Z22QKE/Loopy+dingles.png gallery - loopy dingles a 3D loopy curve is adorned with parallel normal curves and lots of binormal struts with a colored ball on the end of each one. https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1640282793132-Q4S89X0KTDDVAEDDC56X/divisor+spiral+stack+1200.jpg gallery - Divisor Stack Spiral each spiraling spoke of length n has all of its divisors sitting on top of it. some n have lots of sitters, primes have just 1. there are 60 numbers in each revolution, 196 is the last n. what do you notice? can you see the primes? which n has the most divisors? https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1640282793904-DO5H3RV9ORBHYDCF70GN/Hilbert+soap+film+1800+fade+.jpg gallery - hilbert soap film the 3d hilbert curve is the limit of square-cornered paths that increasingly fill up the unit cube. i told mathematica to replace the paths with spline curves. here we have hilbert splines 1, 2, and 3, joined by soap films between the 1-2 and the 2-3. the films then cast a translucent shadow on the beach. https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1640304523706-HICUBFVLVIUS8C0FVF2Q/Superloop+vines+w+shadow.jpg gallery - vine superloop A central loopy tube, defined by trig functions, is surrounded by a long green vine, which has sprouted a few hundred leaves. The tube is called a 3D lissajous figure, and it helps line up the leaves, which are flat cylinders. The shadow is fake, just the original image compressed and skewed for perspective. https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1640305022781-J2RS8DZCGUEG6IHOM9X5/Dodeca+Diagonals+1200.jpg gallery - dodeca diagonals The Platonic dodecahedron (blue) shows off its space diagonals of all possible lengths. The sphere barges in and obscures a lot of them, but you can imagine them fighting for space in the center of the picture. https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1640306638369-SVTW5BG9P4GQ1GEU8RXL/Saddle+normal+binormal+curves+1200.jpg gallery - saddle normals and binormals The red saddle curve has a tangent direction, then a normal direction towards the center of curvature, and also a binormal direction perpendicular to the first two. Parallel curves in both directions give this object its depth, and a few Moiré patterns as well. http://www.dansmath.com/blog daily 0.75 2023-04-08 http://www.dansmath.com/blog/2021/3/5/my-talk-at-u-of-santa-clara-2020 monthly 0.5 2022-01-16 https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1614979440322-MQQ9XTG4G6H6BW02MT5V/Screen+Shot+2021-03-05+at+1.23.26+PM.png dan's blog - my talk at Santa Clara u - spring 2020 Space can be filled with concentric octahedral shells. Each shell has lattice points that can be visited by a single route, and the path can then jump out to the next shell. https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1614978982999-CXFL2VVBM2YAHOIT2CO0/pastedGraphic.png dan's blog - my talk at Santa Clara u - spring 2020 Ulam’s Spiral extended along the sides and bottom of a cube https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1614979311395-96L6OSDAO7KRIKTREK9I/3__%23%24%21%40%25%21%23__pastedGraphic.png dan's blog - my talk at Santa Clara u - spring 2020 Net for tiled octahedron shown below, copies passed out to the audience! https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1614979177861-8K358UUNOYJTPYDEHFX8/2__%23%24%21%40%25%21%23__pastedGraphic.png dan's blog - my talk at Santa Clara u - spring 2020 Eulerian String Figure Octahedron (L) and Sloppy Fourier Cube (R) https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1614979645809-L3QVEJ12HTNFCC51BFCL/Zigzag+Octahedron+900.jpeg dan's blog - my talk at Santa Clara u - spring 2020 “Zig-Zag Octahedron” - My entry for the Joint Mathematics Meetings 2021 (Virtual) Math Art Exhibition http://www.dansmath.com/blog/2021/4/16/joint-math-meetings-2018-san-diego monthly 0.5 2022-01-16 https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1642362240734-1BPC3XU68L999J5ZC7AA/IMG_1265.jpg dan's blog - joint math meetings 2018 (san diego) - Make it stand out After seeing the total eclipse in Oregon the summer before, the conference floor seemed even brighter. https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1642360172938-A83KCELDRAR8ZDLNYZGF/Slinky+Spheres.jpg dan's blog - joint math meetings 2018 (san diego) - Make it stand out “Slinky Spheres” by Dan Bach. Twenty colored spheres are cradled inside a web of toroidal helices formed from the normal and binormal vectors along a central wiggle (not pictured). The wiggle also contains the centers of the spheres, which is only fair. https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1642360825897-2JH02UZ3W7SCOSMDS8M5/Prime+Bead+Spirals.jpg dan's blog - joint math meetings 2018 (san diego) - Make it stand out “Prime Bead Spirals” by Dan Bach Starting at the bottom, strings of 1000 beads are formed into a disk, cylinder, cone, and “parabowla.” Primes are green, composites are yellow. The last prime in each string is 997. Why do the green beads line up better on the cylinder? (There are 60 beads per rotation on the cylindrical helix.) http://www.dansmath.com/blog/2021/2/28/my-math-art-career-begins monthly 0.5 2022-05-25 https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1614540973133-36VTY7IQHUKO9S7N9HUZ/dan_bach_entry+1%C2%A9+small.png dan's blog - my math art career begins! (Atlanta) “A Fine Mesh We’re In” by Dan Bach, 2016 A central curve (not shown) has tangent, normal, and binormal directions at each point, making a local {T, N, B} frame. Using a trigonometric combination of the N and B vectors, we describe a toroidal mesh of curves with hues of green, yellow, and orange. Spheres of varying colors and sizes are placed along an equatorial helix and some try to escape their bonds. https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1653498408863-BRR5J31SI4ASATSTR6PQ/entry_2_1800s.jpg dan's blog - my math art career begins! (Atlanta) - Make it stand out “Growing Parallel Normal Curves” by Dan Bach, 2016 The starting red curve has a center of curvature at each of its points. The colored parallel curves go toward that center in increasing amounts. Some groups of curves are rotated, some are reduced in number, but all originate from the same ball-shaped bundle at the top, appropriately used as the dansmath.com logo. http://www.dansmath.com/blog/2021/2/28/ibooks-author-conference-2016 monthly 0.5 2022-01-04 https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1641337674618-7YXZFAE3OK9HWZZHRV99/Nashville+Talk_key.png dan's blog - ibooks author conference 2016 - Make it stand out Slides from my featured talk, creating 3D Math Art inside of an Apple iBook. They don’t want you to call it that. https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1614544421653-GY2R5N1KPZYSLOU38MO0/Book+cover.jpg dan's blog - ibooks author conference 2016 Above: The cover of my interactive book, part of the Math You Can Handle series. http://www.dansmath.com/blog/2016/1/27/pattys-calculus-videos monthly 0.5 2020-03-25 https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1453922883901-X8OEIY0RGOJAMYMA7E4N/image-asset.png dan's blog - watch patty's calculus videos Let Patty take you on a video journey through the land of calculus, clearly explaining the topics in her friendly style. http://www.dansmath.com/blog/2015/12/27/view-dansmath-models-on-cardboard monthly 0.5 2015-12-27 https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1451246180331-EYYPSFTCVISJ7ESI5AJW/saddle+wires+cardboard.jpg dan's blog - view dansmath models on cardboard! Tap the image on your phone and put it in a Google Cardboard viewer. http://www.dansmath.com/blog/2015/12/21/dansmath-3d-logo-embedded-here monthly 0.5 2015-12-27 https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1451244519137-LQO3PYG12WSY4K9DF2IE/image-asset.png dan's blog - dansmath 3D logo embedded here! One of my 3D models on Sketchfab, completely rotatable. Click image to go to my local models page. http://www.dansmath.com/blog/2015/9/26/dansmathblog monthly 0.5 2015-12-27 https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1451245081719-XOJPTIGOL4Z23SWTWHKX/image-asset.jpeg dan's blog - dansmath.com - it's on! http://www.dansmath.com/blog/category/art+exhibitions monthly 0.5 http://www.dansmath.com/blog/tag/dansmath monthly 0.5 http://www.dansmath.com/blog/tag/Atlanta monthly 0.5 http://www.dansmath.com/blog/tag/cardboard monthly 0.5 http://www.dansmath.com/blog/tag/geometry monthly 0.5 http://www.dansmath.com/blog/tag/math monthly 0.5 http://www.dansmath.com/blog/tag/mathart monthly 0.5 http://www.dansmath.com/lessons daily 0.75 2016-02-14 https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1450561341320-VSZPUUNN4DERSDY1T16M/image-asset.gif dan's math lessons https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1450983348986-JAQRIW3HTG34FRDET48H/image-asset.gif dan's math lessons   Locate the list of points on the graph. https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1450983221505-UEW775DYPLLV8F9HSD57/image-asset.gif dan's math lessons https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1450658420126-3HYUFYS6K4H0VPFPUBH5/image-asset.gif dan's math lessons octahedron < 3, 3, 3, 3 > 8 triangles https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1450634993855-516MW6DXL8Q4DA2YFEVM/f_x.gif dan's math lessons   General function, at most one y for each x. https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1450636391111-LBE8RAK04R18QDWRFDDD/3__6.gif dan's math lessons https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1450636391125-FB05M6UVER4LM6PVUQFK/4_4_4_4.gif dan's math lessons https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1450636391535-QHVVTAY5ZMPZCJGM2T6M/6_6_6.gif dan's math lessons https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1450658901994-QGXJ015227Y8C5DSQDZG/icosa2.gif dan's math lessons icosahedron < 3, 3, 3, 3, 3 > 20 triangles https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1450638516075-RV9WO34JWYPD690B762H/3_3_3_3_6.gif dan's math lessons - <3,3,3,3,6> <3,3,3,3,6><3,3,3,3,6> https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1450637999306-B32MB2XXE3Z7I7O6155E/eyeballs.gif dan's math lessons - Does this exist? <3,3,6,6> https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1450637915751-R10G6959BPZMR5FOAIXN/3_6_3_6.gif dan's math lessons https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1450637915207-KB49WHZR1LKWHXOZJC6T/3_3_3_4_4.gif dan's math lessons https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1450637915440-QEH6OEGTM4E9WWODJQQT/3_3_4_3_4.gif dan's math lessons https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1450637915580-2ZSR1UA1XW0B4JZISVAT/3_4_6_4.gif dan's math lessons https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1450637916086-FBT66DVE4FKV4P0XX7B8/4_8_8.gif dan's math lessons https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1450637915857-DKCTGM7L8KZOKJA6M9P0/3_12_12.gif dan's math lessons https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1450637915969-5D29PF84BAQZWPKHY9B3/4_6_12.gif dan's math lessons https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1450658627570-9U9ABLPALD1R0PGCS3KG/image-asset.gif dan's math lessons hexahedron < 4, 4, 4 > 6 squares https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1450659162523-MMPR4DPPCZ7RB91Q0VIO/dodec2.gif dan's math lessons dodecahedron < 5, 5, 5 > 12 pentagons https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1450635477956-MHA5SG7A2F4KJWQ632YF/image-asset.gif dan's math lessons The x and y coordinates always add up to 2. https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1450635090488-WNMB849MKU5DXK22413S/image-asset.gif dan's math lessons The y is always twice the x. https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1450657844726-BHZC8HPNPM6X5ZDTOO34/image-asset.gif dan's math lessons tetrahedron < 3, 3, 3 > 4 triangles https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1454119077388-TLW0MT4EBC7ECGWHYWLV/image-asset.gif dan's math lessons https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1454781605775-6PD022VUFJNZROLHKW4Z/image-asset.gif dan's math lessons limaçon r = 1 + 3 cos t https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1454780429771-2SS2V4KX5ADU3X0UKSMD/image-asset.gif dan's math lessons https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1454781692588-TMPS1Q5GW7S8G8JYH130/image-asset.gif dan's math lessons spiral r = t / 5 https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1454781512584-ER2QNMCBPNNVK3BCGWLO/image-asset.gif dan's math lessons cardioid r = 2 + 2 cos t https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1454781865671-EISPEOW4GZZJ8BHW4FXO/image-asset.gif dan's math lessons petal curve even r = 3 cos 2t https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1454782510004-EH6MWWXRO7BMT3NQXS6P/image-asset.gif dan's math lessons bach's bug r = 2 cos 3t + 2 sin 4t https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1454781343942-AR2DEAC1NJRSZASC7H73/image-asset.gif dan's math lessons circle r = 3 https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1454700184421-0C77LA83FVNO2U9UGB8Q/image-asset.gif dan's math lessons This is like a vibrating guitar string held in the middle. https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1454781927595-R1LB3ZS2HGEZH5S4ANQP/image-asset.gif dan's math lessons ellipse r = 5 / (2 + cos t) https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1454781754646-FAC1LH2S38FEQRP3B4SX/image-asset.gif dan's math lessons petal curve odd r = 4 cos 3t https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1454699960288-X0B5OBIY5E4FJBKG6EYB/image-asset.gif dan's math lessons This sine wave animated GIF has been running continuously since 1997! https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1454779296274-DU1PIR01KDEIVWFUWZEL/image-asset.gif dan's math lessons More like a compressed spring than a vibrating string. https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1455388305345-Z0NHRZU5GUD4F6KQIYYH/image-asset.gif dan's math lessons The red secant lines PQ approach the blue tangent line at P. https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1455144039920-U8BE2BDAYWVVOWHBPRLH/image-asset.gif dan's math lessons Your basic parabola; the y is the square of the x. https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1454956085704-1E515A8QAYB8NXADBSY2/image-asset.gif dan's math lessons y = 2^x or f(x) = 2^x exponential function https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1455143353487-CRONDHMTTA74JXMRSUG3/image-asset.gif dan's math lessons Try and connect the location of the vertex with the equation of the graph. https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1455144339950-ORIZHYGXYKU23OYQLCHN/y_2_to_x.gif dan's math lessons An exponential function; the height doubles as x increases by 1. https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1454956333702-NRES1AYOK924UWIYO0RY/y_2.gif dan's math lessons y = 2 or f(x) = 2 constant function https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1454955889740-EPZNVQ6VX6LRLD2XSY7L/y_2x.gif dan's math lessons y = 2x or f(x) = 2x linear function https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1454955702743-3A1Z56Q4BYSXXEWT9BDJ/f_x.gif dan's math lessons The red curve consists of all points (x, f(x)) for the set of x's we choose. https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1454956021935-VRQHRNBB67RH7BC9ITPC/image-asset.gif dan's math lessons y = x^2 or f(x) = x^2 quadratic function https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1453575414228-AHMSWA2UZ1AYH1GXTX44/PCV+playlist+2.png dan's math lessons The derivative is the central concept in calculus. Patty explains the definitions and computational techniques for finding the derivative of a function. https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1453575579484-HF1MWU06Q820KPPLD1SN/image-asset.png dan's math lessons Integrals are in some sense the opposite of derivatives. Patty shows you how the "anti-derivative" can actually help to compute the area under a curve y = f(x). https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1453575350478-VGWFQQEYJYI8ZG9927C4/PCV+playlist+1.png dan's math lessons An introduction to the concept of limit. What do function output values "approach" when the input variable gets "close" to some number? What about infinity? https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1453575543316-TZKBQTZII5OJUU73W86B/PCV+playlist+3.png dan's math lessons "But what is it good for?" is the question on some students' minds. Well-chosen applications illustrate how the derivative can be used to solve interesting problems! http://www.dansmath.com/podcast daily 0.75 2018-01-06 https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1450744659803-TTJR9KFJ4N868VTNTBMR/mathcast+light.gif dansmathcast http://www.dansmath.com/problemsanswers daily 0.75 2017-08-13 https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1502645790418-VWK6QB40117IDOO95HQV/image-asset.gif answers https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1502645818631-NIYH3P3IP0EMV19DRO1M/image-asset.gif answers http://www.dansmath.com/problems-only daily 0.75 2017-08-13 https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1452927008499-R2DQWIZ5BQSAX3XFS25J/image-asset.gif problems https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1452927048023-7QPAV0TANLBB77GBHU7K/image-asset.gif problems https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1502643464364-KH9R0H04WCS70DPGNKBG/prob39a.gif problems https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1502643545113-DCGK114AGU4JKRDW0TB1/image-asset.gif problems http://www.dansmath.com/feature-pages daily 0.75 2019-03-02 https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1477329808705-JYTVGHR6MAL660NNHBO4/image-asset.jpeg featured My first entry in the Bridges Math Art contest, for the 2017 Joint Mathematics Meetings in Atlanta. https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1500164718504-Y9WXZWJRYVDBY9UMWUA6/beadtwist.gif featured - color bead spin each concentric circle of beads revolves faster toward the center, but what's happening with the colors? https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1551551134335-Z94GWCZHBFIU8UPIUCKZ/cube_tiles.gif featured - cube tiles the tiling of a 32 x 33 rectangle, by nine incongruent squares, suddenly jumps out of the plane and plays around in space. you won't believe what happens next! (drawn in mathematica, cropped at ezgif.com) https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1500164998889-CI1BR9JLUN0SBKPWI4S6/SaddleMorph4.gif featured - color beads morph a string of colored spheres change shape, from simple ring, to saddle curve, to other loopy shapes. drawn in mathematica and saved as an animated gif. https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1500164721970-FFCVVC8ATMXALAYY52XV/circleblink.gif featured - circle blink animation forty-one colorful circles narrow into ellipses and back again, in perfect concert. is 41 the sum of two squares? drawn in mathematica and exported as a gif. or is it a jif? https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1500164770345-EMU4YGAP4ORTNHK4N708/LayerBeads4.gif featured - layer beads animation colored balls dot the landscape, in a row, then a layer, then a whole cube. drawn in mathematica (and exported as a gif of course). see if you can "spot" the size, color, and saturation values before they disappear! https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1500165051951-0R9B7OWST657DWLYPHDT/TetraPlay.gif featured - tetra-playa-hedron playing around with central vectors forming a tetrahedron, showing its four facial incircles, and some bubble that appears out of nowhere. what's with the bubble? https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1500165098162-OTLEPP81JLE1VJN7TJXW/TubeUnroll.gif featured - unrolling a beaded tube over 200 colored spheres form themselves into a tube which first unrolls, then... you won't believe what happens next! https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1551552799262-LZP3UL3ATHOGWCKQF5EJ/octapop.gif featured - octahedron deconstructed an octahedron has eight triangles (yellow, F=8), twelve edges (green, E=12), and six vertices (blue, V=6). watch them form the shape all at once, set by set, or piece by piece. figure out what V - E + F is, for this and other polyhedra! https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1551553339157-4UI991Y5H8FU3YFA9US1/LoopShadows.gif featured - loopy shadows watch in awe as one 3d lissajous curve spins and morphs into another, and back! shadows are cast from invisible sources onto two walls and the floor. keep trying to count the loops until just before your eyes give out! https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1500164718504-Y9WXZWJRYVDBY9UMWUA6/beadtwist.gif featured - color bead spin each concentric circle of beads revolves faster toward the center, but what's happening with the colors? http://www.dansmath.com/mathgifs-1 daily 0.75 2018-06-25 https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1529946791043-XI9N33LS0U261NK30FGT/Crooked+cubes4.gif mathgifs - crooked cubes the eight vertices (corners) of a cube wander around their assigned position, changing the square faces into trapezoids and rectangles. the official unit cube (pink) sits there, unperturbed, while the crazy crooked (green) cube intersects with it, and other surprises ensue. can you figure out whether the volume of the crooked cube is changing? https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1529946791043-XI9N33LS0U261NK30FGT/Crooked+cubes4.gif mathgifs - crooked cubes the eight vertices (corners) of a cube wander around their assigned position, changing the square faces into trapezoids and rectangles. the official unit cube (pink) sits there, unperturbed, while the crazy crooked (green) cube intersects with it, and other surprises ensue. can you figure out whether the volume of the crooked cube is changing? https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1529946876011-SA4GGJ0OJODS9QRK490B/cuboctapath1.gif mathgifs - cuboctahedron with worms a cuboctahedron has two squares and two triangles meeting at each vertex. so it has four edges at each corner ball, allowing for an eulerian circuit, a path that traces all edges exactly once. these three colored worms chase each other around the play structure, forever! https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1529947025229-0D0R7UZQ2DLEXNVNL4PG/newredblue2.gif mathgifs - exploding parabola the classic case of red vs blue... but this overlooks all the other colors that can spring up! rainbow beads follow trigonometric paths in space, drawn in mathematica. https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1529947711551-3C70CCPSXEOL98YU0TP2/Dodeca_squirm.gif mathgifs - squirming dodecahedron what happens if you let the vertices of a polyhedron wander around in circles? the edges have to strain to stay connected, and the faces may not all be planar, but don't judge. there are 12 "faces" and 20 wiggling green vertices. can you find how many edges there are, without counting? http://www.dansmath.com/shopinfo daily 0.75 2020-03-25 https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1500681752033-JMIX9F7UZ0I9CPEHKP1X/Purple_surf.png dansmathshop surfaced curves, and more! https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1500681905806-XZEGY6X9JS2VPU4KCJAL/IMG_1638.jpg dansmathshop math you can handle, literally! https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1500682862172-XFRS0RU9M4EL2S2FDUS1/Screen+Shot+2017-07-21+at+5.20.34+PM.png dansmathshop math art, for your actual desktop! https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1443287802999-Y92BT9URNYB9TFQGQVVZ/image-asset.png dansmathshop This is a top view of a 3D bundle of curves based on a wiggly circle (red). http://www.dansmath.com/home daily 1.0 2025-06-29 https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1657857097627-P9RBAPAFJXQ92SFVOMZJ/dansmath+logo+w+text.jpg dan's math home - gallery gallery https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1640155199811-BXK11SDOFIKIUV8V2YRU/Dan%2BDenver%2BJMM20.jpg dan's math home - art shows art shows https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1657857328777-QT0NB9L1DENF0V4RGSS1/Book%2Bcover.jpg dan's math home - books books https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1515124742309-SQ12DGT12AI87JK55SP8/IMG_0035+%281%29.jpg dan's math home - buy art buy art http://www.dansmath.com/thumb-gallery daily 0.75 2021-12-23 https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1443307052398-3VYDBYWZTXKTW87TKPW2/dansmath14.jpg gallery - dan and the giant sphere at a small hideaway in sonoma, california lives a metal sphere apparently about 7 feet in diameter, and hence about 22 feet around. that's an interesting pattern on the surface. any guess as to how many little shapes cover the sphere? my hand fits through one of them. is it a polyhedron? https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1640282796329-Y78HUQOPER0B38X84CZS/Saddle+Firebird+1500.jpg gallery - saddle firebird the basic saddle (x, y, z) = (cos(t), sin(t), cos(2t)) is adorned with hundreds of sine waves based on the tangent, normal, and binormal vectors. trig functions attached to the {T, N, B} frame tell the story here. https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1476893836411-K31CNO2NCLEZYSBVO48D/3D+star+1.png gallery - dansmath logo (3D star - top view) starting with the outer red curve (a slightly wiggly circle), the curves change color as they march inward toward the center of curvature at each point. the slight wobble is magnified, especially vertically, as the curves go from orange to blue-green. this object has become my go-to lo-go. https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1477427425564-QABFCO3TCFCAV27KILQP/Balls+in+a+basket+small+sq.png gallery - spheres in a wire basket i dreamed up a twisty central curve and made mathematica draw the curves around it, with weird combinations of the T, N, B vectors doing the job. the spheres are sized to just touch the wires. https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1640282796255-4LW650FACE7HM5KUYV2O/Many+fewer+circles+half+rings+900.jpg gallery - circles in space there are lots of circles in this picture, but NONE OF THEM touch any others! based on a 1983 article I rescued from an old pile of AmerMathMonthly, I told Mathematica to put circles on each spherical shell that avoid the intersection with the vertical red rings. https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1551556720003-74PKA1VCOZEV3W5D2HNT/demi-3.png gallery - demiregular tiling made in girih.app - this tiling of triangles, squares, and hexagons can be extended to fill the whole plane. https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1476893643145-24KDVI6UBB6WN3Z22QKE/Loopy+dingles.png gallery - loopy dingles a 3D loopy curve is adorned with parallel normal curves and lots of binormal struts with a colored ball on the end of each one. https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1640282793132-Q4S89X0KTDDVAEDDC56X/divisor+spiral+stack+1200.jpg gallery - Divisor Stack Spiral each spiraling spoke of length n has all of its divisors sitting on top of it. some n have lots of sitters, primes have just 1. there are 60 numbers in each revolution, 196 is the last n. what do you notice? can you see the primes? which n has the most divisors? https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1640282793904-DO5H3RV9ORBHYDCF70GN/Hilbert+soap+film+1800+fade+.jpg gallery - hilbert soap film the 3d hilbert curve is the limit of square-cornered paths that increasingly fill up the unit cube. i told mathematica to replace the paths with spline curves. here we have hilbert splines 1, 2, and 3, joined by soap films between the 1-2 and the 2-3. the films then cast a translucent shadow on the beach. https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1640304523706-HICUBFVLVIUS8C0FVF2Q/Superloop+vines+w+shadow.jpg gallery - vine superloop A central loopy tube, defined by trig functions, is surrounded by a long green vine, which has sprouted a few hundred leaves. The tube is called a 3D lissajous figure, and it helps line up the leaves, which are flat cylinders. The shadow is fake, just the original image compressed and skewed for perspective. https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1640305022781-J2RS8DZCGUEG6IHOM9X5/Dodeca+Diagonals+1200.jpg gallery - dodeca diagonals The Platonic dodecahedron (blue) shows off its space diagonals of all possible lengths. The sphere barges in and obscures a lot of them, but you can imagine them fighting for space in the center of the picture. https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1640306638369-SVTW5BG9P4GQ1GEU8RXL/Saddle+normal+binormal+curves+1200.jpg gallery - saddle normals and binormals The red saddle curve has a tangent direction, then a normal direction towards the center of curvature, and also a binormal direction perpendicular to the first two. Parallel curves in both directions give this object its depth, and a few Moiré patterns as well. http://www.dansmath.com/new-gallery daily 0.75 2021-12-23 https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1443307052398-3VYDBYWZTXKTW87TKPW2/dansmath14.jpg slide gallery - dan and the giant sphere at a small hideaway in sonoma, california lives a metal sphere apparently about 7 feet in diameter, and hence about 22 feet around. that's an interesting pattern on the surface. any guess as to how many little shapes cover the sphere? my hand fits through one of them. is it a polyhedron? https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1640282796329-Y78HUQOPER0B38X84CZS/Saddle+Firebird+1500.jpg slide gallery - saddle firebird the basic saddle (x, y, z) = (cos(t), sin(t), cos(2t)) is adorned with hundreds of sine waves based on the tangent, normal, and binormal vectors. trig functions attached to the {T, N, B} frame tell the story here. https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1476893836411-K31CNO2NCLEZYSBVO48D/3D+star+1.png slide gallery - dansmath logo (3D star - top view) starting with the outer red curve (a slightly wiggly circle), the curves change color as they march inward toward the center of curvature at each point. the slight wobble is magnified, especially vertically, as the curves go from orange to blue-green. this object has become my go-to lo-go. https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1477427425564-QABFCO3TCFCAV27KILQP/Balls+in+a+basket+small+sq.png slide gallery - spheres in a wire basket i dreamed up a twisty central curve and made mathematica draw the curves around it, with weird combinations of the T, N, B vectors doing the job. the spheres are sized to just touch the wires. https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1640282796255-4LW650FACE7HM5KUYV2O/Many+fewer+circles+half+rings+900.jpg slide gallery - circles in space there are lots of circles in this picture, but NONE OF THEM touch any others! based on a 1983 article I rescued from an old pile of AmerMathMonthly, I told Mathematica to put circles on each spherical shell that avoid the intersection with the vertical red rings. https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1551556720003-74PKA1VCOZEV3W5D2HNT/demi-3.png slide gallery - demiregular tiling made in girih.app - this tiling of triangles, squares, and hexagons can be extended to fill the whole plane. https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1476893643145-24KDVI6UBB6WN3Z22QKE/Loopy+dingles.png slide gallery - loopy dingles a 3D loopy curve is adorned with parallel normal curves and lots of binormal struts with a colored ball on the end of each one. https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1640282793132-Q4S89X0KTDDVAEDDC56X/divisor+spiral+stack+1200.jpg slide gallery - Divisor Stack Spiral each spiraling spoke of length n has all of its divisors sitting on top of it. some n have lots of sitters, primes have just 1. there are 60 numbers in each revolution, 196 is the last n. what do you notice? can you see the primes? which n has the most divisors? https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1640282793904-DO5H3RV9ORBHYDCF70GN/Hilbert+soap+film+1800+fade+.jpg slide gallery - hilbert soap film the 3d hilbert curve is the limit of square-cornered paths that increasingly fill up the unit cube. i told mathematica to replace the paths with spline curves. here we have hilbert splines 1, 2, and 3, joined by soap films between the 1-2 and the 2-3. the films then cast a translucent shadow on the beach. https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1640304523706-HICUBFVLVIUS8C0FVF2Q/Superloop+vines+w+shadow.jpg slide gallery - vine superloop A central loopy tube, defined by trig functions, is surrounded by a long green vine, which has sprouted a few hundred leaves. The tube is called a 3D lissajous figure, and it helps line up the leaves, which are flat cylinders. The shadow is fake, just the original image compressed and skewed for perspective. https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1640305022781-J2RS8DZCGUEG6IHOM9X5/Dodeca+Diagonals+1200.jpg slide gallery - dodeca diagonals The Platonic dodecahedron (blue) shows off its space diagonals of all possible lengths. The sphere barges in and obscures a lot of them, but you can imagine them fighting for space in the center of the picture. https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1640306638369-SVTW5BG9P4GQ1GEU8RXL/Saddle+normal+binormal+curves+1200.jpg slide gallery - saddle normals and binormals The red saddle curve has a tangent direction, then a normal direction towards the center of curvature, and also a binormal direction perpendicular to the first two. Parallel curves in both directions give this object its depth, and a few Moiré patterns as well. http://www.dansmath.com/original-site daily 0.75 2015-10-02 https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1443320159373-HNYC3IVTY13EQB9T3NRD/title.gif original - old home https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1443320159021-ACRGHGARLB83ETMXXPU4/mathcasm.gif original - dansmathcast mathematics for the masses in a half hour you'll be smarter! https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1443320158648-A81LQC9VI8QFC0UME2AU/blog_button.jpg original https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1443320159189-71M9M55X9TGSL2TG36B2/prealpicsm.jpg original https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1443320158822-FHRCM52GQ7P730NHH86U/infobutn.gif original https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1443320159081-MS6V8XTOE1I2XZQ8YOMV/meetbutn.gif original https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1443320158649-VOHA3C6454UX2Y1F0X9H/askbutn.gif original https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1443320158971-KO66S5HERJT4MVEMXQB7/lesnbutn.gif original https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1443320159135-DLQ5BF150DG7CD5DD398/mtcabutn.gif original https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1443320158775-4C1F5GK97VIXT9X42QHH/dvcbutn.gif original https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1443320159322-0BEJUP88J9T41AQ6K4PY/prwkbutn.gif original http://www.dansmath.com/books daily 0.75 2021-12-16 https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1443828662474-PSLALFDSOHHYY2LQ2IAC/dan_board.jpg dan's math books dan bach "the math jock" https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1472242271568-8UL42H54CAAXQ0Y59IFR/image-asset.jpeg dan's math books https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1472502315889-XKKG0VCI685ZRRT65OHK/image-asset.png dan's math books https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1443320722055-HOZI4HW3DETMM3BS6ZJ9/prealpicsm.jpg dan's math books - Prealgebra - Mathematics for a Variable World co-written with Patricia Leitner, this book provides a gradual transition from the concrete patterns of arithmetic to the abstract notions of algebra. https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1443320679426-4U3HYJ6NP4FUJ17U60UE/Screen+Shot+2015-09-26+at+7.23.07+PM.png dan's math books - Beginning Algebra Solutions for a Variable World by Dan Bach http://www.dansmath.com/models daily 0.75 2018-05-16 http://www.dansmath.com/pattys-calculus-1 daily 0.75 2022-08-10 https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1453913024742-8ZYEV9R89WQIOEZ6KG1S/image-asset.png patty's calc vids Patty Leitner has been making instructional math videos for decades, and you can link to her calculus videos here! http://www.dansmath.com/playlist-1 daily 0.75 2022-06-04 http://www.dansmath.com/about-dan daily 0.75 2021-12-16 https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1453915512737-HHPCDMNQ4OW7IFVRR1E7/image-asset.png about dan - dan bach, back in his teaching days - diablo valley college, northern california http://www.dansmath.com/playlist-3 daily 0.75 2016-01-27 http://www.dansmath.com/playlist-2 daily 0.75 2016-01-27 http://www.dansmath.com/playlist-4 daily 0.75 2016-01-26 http://www.dansmath.com/bookupdates daily 0.75 2016-08-26 https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1472242106099-ZA50AMOL5YGALITSEXGA/image-asset.jpeg bookupdates dan's multi-touch iBook "3D Curves and Surfaces" is available on Apple's iBooks Store. http://www.dansmath.com/my-art-shows daily 0.75 2024-05-24 https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1599543016731-80OEKBYLNNGPVKY6GWQK/Dan+%26+Ken+Ribet+JMM.jpg art shows dan at JMM 2019 (with prof Ken Ribet) https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1551554144498-G223DIAFWLXIWTT3L5WW/DanArt.jpg art shows joint math meetings baltimore, md (jan 2019) String Circuit Polyhedra Average Smoothed Saddles https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/cc547764-702c-48ef-8789-be687e80bc0d/IMG_6207.jpg art shows - Make it stand out maa golden section meeting santa rosa JC (feb 2023) A Cubic Foot of Primes https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1639637892890-Q49EDQBOF0JCI5RMNKDV/Dan+JMM+21.jpeg art shows - Make it stand out joint math meetings virtual (jan 2021) Saddle Circles Zigzag Octahedron I designed the catalog & cover! https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/07288153-e37f-4c5f-b488-cf1626eaea02/IMG_7134.jpeg art shows - Make it stand out bridges math art expo halifax, NS, canada (jul 2023) Polygonal Knot Splines https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1599542558539-6EB4MLBT15DIA4PARHQN/Dan+Bridges+2020+small.jpeg art shows bridges math art virtual show (on a bridge, aug 2020) Vine Superloop https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/9f069a9a-6ff2-4515-988c-3cf1c0e70ce2/IMG_8141.jpeg art shows - Make it stand out montclair art walk oakland, calif. (april 2024) First public show & art sale! https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1551556050037-ETEV5ED4CBFIY7J6Z5C9/IMG_0035.jpg art shows bridges math art expo waterloo ontario (jun 2017) Square Gets Loopy (other items for auction) https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/a8b8167e-a667-4e08-b74e-2ae939c7e9d7/Seven+Stylin%27+Saddles+1800.jpg art shows - Make it stand out joint math meetings virtual (april 2022) Seven Stylin’ Saddles https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/ce61e887-d34c-494b-bb4b-21826c20c278/Prime+Log+Spirals.jpg art shows - Make it stand out joint math meetings boston, mass. (jan 2023) Dan’s Prime Logs Prime Log Spirals https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1551554334192-YRWEVR8DCG5HVYPJGANF/Dan+at+USF.jpg art shows book talk at USF san francisco (2017) https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1599537077958-L385ZGHK4ED86WR4MXPN/IMG_1265.jpg art shows joint math meetings san diego, ca (jan 2018) Slinky Spheres https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1551554748739-2ECSF9I2I7M96RWW38TV/51.jpg art shows bridges math art expo stockholm, sweden (jul 2018) Eulerian String Circuit https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/d82642e8-1dc2-47af-aa9f-fec16d35a470/Dan%27s+Prime+Logs.jpg art shows - Make it stand out Whatever it is, the way you tell your story online can make all the difference. https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1639638357076-ECOSPRKX6NUBZHTEJ6BO/Screen+Shot+2021-02-27+at+3.02.30+PM.png art shows - Make it stand out maa golden section meeting virtual GatherTown (feb 2021) Interpolation Surfaces Dan’s Divisor Stack Spirals https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1599543278563-UJ0FNCSFCRO8UX2816JV/Screen+Shot+2020-09-07+at+10.34.04+PM.png art shows maa golden section meetings santa clara univ (apr 2017) Growing Parallel Normal Curves https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1599538088464-TLS0FY529RT65FZGHWSZ/IMG_0771.jpg art shows bridges math art expo linz, austria (july 2019) Fourier Square Mountains https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1599538900088-UWQR62AMQ5HSZR33KW0N/Dan+Golden+2019.JPG art shows maa golden section meeting fry’s, saratoga, ca (feb 2019) Sloppy Fourier Cube https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1599539201307-ZDRMCV8NTOEW9EYZH9J7/Dan+Denver+2020.jpg art shows joint math meetings denver, co. (jan 2020) Nested Sphere Towers Fraction Cylinders https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1551554993823-D7SXTGKEE7ATVFPT8KUJ/IMG_3038.jpg art shows dansmath logo overload https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1c0ad1c3-cc54-42a2-bae9-93af820521f1/Goldbach+Prime+Bars.jpg art shows - Make it stand out maa golden section meeting cal state maritime (feb 2022) Goldbach Prime Bars https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1551554031075-KWAXUT3D29SHR1L2O2MK/Dan+Atlanta+Art.jpeg art shows joint math meetings atlanta, georgia (jan 2017) A Fine Mesh We’re In https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1551555788054-AD5IU4YGLX6CCHX03Z2X/IMG_1647.jpg art shows maa golden section meeting cal state hayward (mar 2018) Xmas Tree Lot Prime Bead Spirals https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1639638897016-JOGCPI9NMVNZGE6EDFL9/Hilbert+soap+film+900.png art shows - Make it stand out bridges math art virtual show Hilbert Soap Film (aug 2021) https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/605a3e69-7566-49cc-84fa-1b15d53a3da5/IMG_7833.jpeg art shows - Make it stand out maa golden section meeting uc santa cruz (feb 2024) Three Banded Glasses Polygonal Knot Splines https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/b349f92c-5838-4dd4-8ebc-f6b72c03ef94/IMG_7597.jpeg art shows - Make it stand out joint math meetings san francisco, calif. (jan 2024) A Cubic Foot of Primes Three Banded Glasses https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1639639287917-IKPBOGD445R4SWKKTGQ0/Disjoint+circles+99.jpg art shows - Make it stand out bridges math art expo helsinki, finland (july 2022) Space-Filling Circles https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/d8f78c36-b4ca-4a38-8ade-6eaeeb857691/IMG_2924.jpg art shows maa golden section meeting mills college, oakland (feb 2020) last public show until 2022) https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/5bd22a87-4bf4-4149-9eba-33f8d0e2a81e/IMG_2680.jpeg art shows - Make it stand out dan at JMM in denver, 2020 http://www.dansmath.com/new-page-2 daily 0.75 2019-12-23 https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1526959399114-GKIQ53GYA4CB8XTIXY4B/3D+star+1.png New Page http://www.dansmath.com/mathshop daily 0.75 2022-10-26 https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1597118069481-HBY8OSBM0IW4YYU8T6CY/divisor+spiral+stack+512.jpeg dansmathshop dan’s divisor spiral https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1597118930233-MYQISX8RC4VB2ICN0U60/Hilbert+Swirl+2.png dansmathshop hilbert square swirl https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1597118458395-BHG3UHFHGU2IEXDF8ADP/Sloppy+Fourier+Cube.jpg dansmathshop sloppy fourier cube http://www.dansmath.com/home-2019 daily 0.75 2020-09-08 https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1526959399114-GKIQ53GYA4CB8XTIXY4B/3D+star+1.png home (2019) - my dansmath logo (top view) (Copy) https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1549062501237-HYHENTBOD2419ITK971X/DanArt.jpg home (2019) - at joint math meetings art show 2019 (Copy) https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1657857328777-QT0NB9L1DENF0V4RGSS1/Book%2Bcover.jpg home (2019) - my interactive 3D mathart ibook! (Copy) https://images.squarespace-cdn.com/content/v1/5606cea3e4b0983210439d58/1515124742309-SQ12DGT12AI87JK55SP8/IMG_0035+%281%29.jpg home (2019) - my art display at bridges 2017, waterloo (Copy) http://www.dansmath.com/artistwebsites daily 0.75 2021-02-26 http://www.dansmath.com/read-me-supply daily 0.75 2025-05-12