You want to walk 10 blocks north and 10 blocks east. It would be shorter to walk along the hypotenuse, but the same distance to walk 1 block north, then 1 block east, then 1 block north, etc. it seems that if the blocks were infinitesimally short, it would approximate the hypotenuse, but alas, walking 10 blocks in one direction and then 10 blocks in the perpendicular direction is the same as dividing it up. What gives?
My eldest child is starting high school. She is in the most advanced math class (a version of geometry) offered by her fairly demanding high school. But my eldest is struggling during the review of algebra -- rate problems, word problems, etc. Concerned because math is cumulative, and I don't want her falling behind. What can I do to help, both with math and with preventing her from becoming discouraged? [more inside]
I'm trying to draw a 3D ellipse with a 2.5D graphics engine (Core Animation layers) which allow me to only compose my ellipse with line segments that must be moved into place using rotations and translations. I'm having trouble with the order of operations and can't get it to draw properly. Any graphics gurus or game programmers out there who can help me? [more inside]
I'm looking for a textual version of a2 + b2 = c2 that is as old as possible, among all the Greek sources. [more inside]
Wizards of Hive, Before I buy that 90" couch from a friend, how can I make sure I'll be able to get it up my L-shaped stairs? Sure, there are a lot of variables. But is there a tool or methodology for figuring this out ahead of time (presuming I know the depth and height of the couch too)? I don't think I have the cardboard to build a mockup. This couch is 50 miles away and can't be returned. Thanks!
I'm drawing/painting a globe (in time lapse, so the sun appears to rise) and trying to figure out what shape, exactly, the longitude (not latitude) lines are when a globe is flattened into a circle (I know I can just trace them, but I've gotten curious). So, the outermost longitude lines are tangent to the circle, they are half-circles, and the centermost line is a straight line from pole to pole, it's the progressively flatter curves in between that I'm trying to figure out. Do they have a name? Are they catenaries? Are they the curves of progressively larger circles? How do I construct them (easily)? Example image: HERE
Here’s a simple computational geometry problem. I am trying to figure out the value at an point of two line segments based off of the values at both of one of the segment’s endpoints. The problem is that I don’t exactly know the
best way of going about finding the value at one of those points.
Here is a reference figure.
(X_C, YC) = F_C
(X_D, YD) = F_D
How can I calculate the value of F_E, where F_E = (X_E, Y_E), where E is the point on the segment CD, where CD intersects with the line AB?
(Extraneous details inside) [more inside]
Math is hard. Please help me with a slope-related problem. [more inside]
Are there an infinite number of 2D shapes? [more inside]
Calling geographers: has anyone applied the idea of topological prominence to population density? [more inside]
I'm looking for an awesome video/discussion topic that relates to street maps - something appropriate for a HS geometry course. [more inside]
I have forgotten basically all of math, and I want to learn it again from the ground up. [more inside]
Consider two rings that are intertwined. (These lie in 3-dimensional space, but when you draw it on paper it looks like a venn diagram.) In 3-dimensional space they cannot be unlinked. The questions is, if you had one more dimension, can you unlink them?
I'd like to be able to watch the Macy's fireworks from my dad's roof on the Upper West Side. How can I figure out if I'll be able to see them? I have some variables, heights, distances, and video... [more inside]
I'm writing a graphics app where I'm generating a simple gear transmission system with a variable number of gears each with variable number of teeth and placed at random orbits around each other. I generate gears in succession, placing and rotating each with respect to its parent/driver gear before moving on to the next. The problem I'm having is how to determine the initial orientation of each subsequent gear such that its teeth are properly meshed with that of its driver. [more inside]
I'm trying to find a website that teaches vector mathematics in lesson form. [more inside]
MathFilter: Is there a relationship between the number of dimensions in a Euclidean space and the number of regular tessellations of that space? [more inside]
I've got a polygon of n points. How can I simplify out noisy edges? [more inside]
can you help me compute the area of a triangle on the sphere? [more inside]
Math filter: How many equally sized rectangles will fit into a circle, and how should I arrange them in order to make the best-looking approximation? [more inside]
My geometry teacher in high school in 1984 showed us this puzzle. I was only half paying attention, but I believe the goal was to draw a line that intersected each segment only once. [more inside]
Help me with the math of two spheres colliding [more inside]
How can I work out if a point x,y,z is contained by a cone ? [more inside]
Vector Geometry Filter: I'm working in matlab and need to transform a surface to match an arbitrary angle. I have the unit vector of the new normal (and the original normal is in the Z axis (0 0 1))...however i'm not sure how to rotate one normal to another (i know, i know, it sounds very simple really...) [more inside]
My room has an angled ceiling. I have measured its height at the highest and lowest points, and I have the dimensions of the room. Help me determine what height the ceiling is at a particular point on the floor, and where exactly the skylight is. [more inside]
Programming/geometry: in a Flash program (you don't need to know Flash to answer this), I'm trying to place rectangular images at random positions on the screen. There are already images on the screen. I need to make sure that the new, randomly-placed images don't obscure the images already there. [more inside]
Is there a specific name for a rectangle which, if you divide it in half, the two halves have the same proportions as the original rectangle? [more inside]
I have a circular patio table with four legs. The paving stones are uneven, so it has always been difficult to set the table in place so it doesn't wobble. I move it regularly, since the shadows from the trees change, and sometimes I want shade, other times sun. I used to mark small dots on the stones so I could set it down quickly. Then I discovered something very interesting--no matter where I put the table, if I simply rotate it around its center, I can very quickly find a steady configuration. But move it from place to place, and it takes all day. This is like the four color map theorem. It works every time, but I haven't figured out why. It might even be tricky to put this into a mathematical format. The table doesn't need to be level, and all four legs needn't be the same height or "at" the same height. The table just can't wobble. Go geeks.
What do you call those three-dimensional geometric novelties, consisting of eight cubes, joined to each other at one edge to form one large cube, whose pieces can be flipped around to display different images on the exterior of the large cube? What is the history of this delightful object? What are the geometric priniciples behind it?
Can you recommend books like Flatland which mix fiction and math and/or explain the mathematical concepts to laymen?
I read Edwin A. Abbott's Flatland this weekend and really enjoyed its fiction and speculative geometry/mathematics. I guess the logical next step would be to read the unofficial sequel, Flatterland, but can any of you recommend other books that similarly twist math and fiction, or just books that explain mathematical concepts or theories to laymen such as myself in ways that are entertaining to read?