trying on a metaphor
Sade Olutola
AnasAbdin
Discoholic 🪩
occasionally subtle
@theartofmadeline
Misplaced Lens Cap
oozey mess
if i look back, i am lost
Lint Roller? I Barely Know Her
KIROKAZE
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ojovivo
Monterey Bay Aquarium
Janaina Medeiros
Love Begins
let's talk about Bridgerton tea, my ask is open
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JBB: An Artblog!
Kaledo Art
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@graphporn
The Google trend for the search query “quadratic formula”.
It repeats in the same pattern every year. Down in summer, up in September, down again in December and up again in spring time before going down again in the summer. And so it goes on forever.
no fucking wya.
thats the dopest shit ive ever seen,
math textbooks are the best
thanks for the helpful commentary
Gabriel’s Horn and the Painter’s Paradox
Gabriel’s Horn is a three-dimensional horn shape with the counterintuitive property of having a finite volume but an infinite surface area.
This fact results in the Painter’s Paradox — A painter could fill the horn with a finite quantity of paint, “and yet that paint would not be sufficient to coat [the horn’s] inner surface” [1].
If the horn’s bell had, for example, a 6-inch radius, we’d only need about a half gallon of paint to fill the horn all the way up. Even though this half gallon is enough to entirely fill the horn, it’s not enough to even coat a fraction of the inner wall!
The mathematical explanation is a bit confusing if you haven’t taken a first course in calculus, but if you’re interested, you can check it out here.
Mathematica code:
x[u_, v_] := u y[u_, v_] := Cos[v]/u z[u_, v_] := Sin[v]/u Manipulate[ParametricPlot3D[{{x[u, v], y[u, v], z[u, v]}}, {u, 1, umax}, {v, 0, 2*Pi}, PlotRange -> {{0, 20}, {-1, 1}, {-1, 1}}, Mesh -> {Floor[umax], 20}, Axes -> False, Boxed -> False], {{umax, 20}, 1.1, 20}]
Additional source not linked above.
The classical homeomorphism between a coffee mug and a doughnut.
A continuous deformation between a coffee mug and a donut (torus) illustrating that they are homeomorphic. But there need not be a continuous deformation for two spaces to be homeomorphic — only a continuous mapping with a continuous inverse. - Source: Homeomorphism.
just some right angles, moving back and forth and stuff
life goal is to be able to do this hairstyle holy hell
The Beauty of Math in Science - Lissajous Curve
Lissajous curve, also known as Lissajous figure or Bowditch curve, is the graph of a system of parametric equations: x = A.sin(a.t + δ) and y = B.cos(bt) The appearance of the figure is highly sensitive to the ratio a/b - Image 3 (3/2, 3/4 and 5/4). For a ratio of 1, the figure is an ellipse, with special cases including circles (A = B, δ = π/2 radians) and lines (δ = 0). Another simple Lissajous figure is the parabola (a/b = 2, δ = π/4). Other ratios produce more complicated curves, which are closed only if a/b is rational. The visual form of these curves is often suggestive of a three-dimensional knot, and indeed many kinds of knots, including those known as Lissajous knots, project to the plane as Lissajous figures. Visually, the ratio a/b determines the number of “lobes” of the figure. For example, a ratio of 3/1 or 1/3 produces a figure with three major lobes (see image). The ratio A/B determines the relative width-to-height ratio of the curve. For example, a ratio of 2/1 produces a figure that is twice as wide as it is high. Finally, the value of δ determines the apparent “rotation” angle of the figure, viewed as if it were actually a three-dimensional curve. For example, δ=0 produces x and y components that are exactly in phase, so the resulting figure appears as an apparent three-dimensional figure viewed from straight on (0°). In contrast, any non-zero δ produces a figure that appears to be rotated, either as a left/right or an up/down rotation (depending on the ratio a/b).
See more at source: Lissajous curve.
Images: 3D Lissajous curve - Lissajous curve - How to Make a Three-Pendulum Rotary Harmonograph by Karl Sims.
Lagrangian Points
The Lagrangian points are the five locations in an orbital system where the combined gravitational force of two large masses is exactly canceled out by the centrifugal force arising from the rotating reference frame.
At these five points, the net force on a third body (of negligible mass) is 0, allowing the third object to be completely stationary relative to the two other masses. That is, when placed at any of these points, the third body stays perfectly still in the rotating frame.
The first image shows the fields due to the first mass, the second mass, and the rotating reference frame. When added together, these fields generate the effective field shown in the second image. The five Lagrangian points are indicated with gray spheres.
The first three Lagrangian points (labeled L1, L2, and L3) lie in line with the two larger bodies and are considered metastable equilibria. L4 and L5 lie 60° ahead of and behind the second body in its orbit and are considered stable equilibria.
Lagrangian points offer unique advantages for space research, and the Lagrangian points of the Sun-Earth system are currently home to four different satellites.
Mathematica code posted here.
Additional sources not linked above: [1] [2] [3] [4] [5]
EXCERPTS >|< Congruent Triangles (1977)
A series of GIFs excerpted from Congruent Triangles, a short animation movie by Bruce and Katharine Cornwell. The video demonstrates with animation the various relationships of angles and sides to congruency in triangles.
We invite you to watch the full video HERE
EXCERPTS by OKKULT MOTION PICTURES: a collection of gifs excerpted from open source/unknown/rare/controversial moving images. A digital humanities project for the diffusion of open knowledge.
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There’s three sides to this awesome story.
new solid geometry (1955 ed.)
