I rewrote the introduction to the fourth dimension, and changed one of the images. The page is now quite a lot different. Next up for revision is the page "From the 2nd dimension to the 3rd dimension".
I made a number of changes to the fourth dimension glossary to fix errors that Polyhedron Dude pointed out, plus added some new words, bringing the total number of words from 102 to 106. Here are the changes:
I changed the terms tridth/tride/trin to trength/trong/tarrow. This is because the tridth series is potentially confusing - it contains the root "tri-" but it is a measure of the fourth dimension, not the third.
I have Added some more terms to the fourth dimension glossary. They are:
I also modified marp, garp, north, and south.
I completely redid the fourth dimension glossary. Here are the changes i made:
I modified the fourth dimension links page and put the different sections of fourth dimension links into subpages.
I have created a forum to discuss the fourth dimension. Head on over and post your thoughts, questions, theories, etc regarding the fourth dimension.
I have added a number of new fourth dimension links on my links page (none of them are marked as new, though).
I checked all the links on my fourth dimension links page and marked the ones that are broken.
I decided there needed to be a name for all of the round and flat shapes that my site deals with. I came up with the term rotatope for an n-dimensional shape that has round and/or flat sides. This is from the Latin root rota- 'wheel' plus -tope akin to polytope. A 2d rotatope is called a rotagon (akin to polygon), a 3d rotatope is called a rotahedron (akin to polyhedron), and a 4d rotatope is called a rotachoron (akin to polychoron). Because of this new name, i decided to rename the pages that had the information about the shapes. I have fixed all the links throughout my site that i could find. If you find any links that point to a moved page, contact me and i'll fix it asap.
I also added the formulas for the volumes and surface areas to the rotatope pages, plus their number series notation and algebraic labelling (see my rotatope classification page). I also added the relevant terms to the glossary.
I checked all the links on my links page and added a couple more, so it's all up to date now. I also modified some entries in the glossary, and added tables to find correspondences easier.
I have expanded the tables on my formulas page to include the fifth dimension. I also added the generic formulas that you can use to obtain the values for n dimensions for the number of k-cubes in an n-cube, and the surface area and volume of an n-sphere.
I figured out how to do greek letters and superscript letters in html, so I changed the formulas on my formulas page to look much nicer.
I created ray-traced images to replace the images I used to use in my introduction to the fourth dimension. Now they are all spiffy looking - color coded and in 3d.
I have just recently finished reading the book "Beyond the Third Dimension" by Thomas Banchoff. It was a pretty good book, and I recommend it for nearly everyone. You can read my review of it here. I also added the rotation matrices for the second, third, and fourth dimensions on my formulas page.
I fixed the applet so that it now runs on microsoft's vm (virtual machine). This basically means that you don't have to download the latest version of java to see my shape intersection applet. So, all of you who were too lazy to go download the latest version of java or were too confused by Sun's confusing website, you will have no trouble seeing it now.
I decided to break into the business of polyhedra. I downloaded Povray for windows and within half an hour or so I was creating some pretty neat looking images. I made an image of a cube, a tetrahedron, and an octahedron, and created a new polyhedra page for them. The dodecahedron and icosahedron are next.
I wasn't happy with the organization of the round and flat shapes page, so I reorganized it again. Now it is organized by shape instead of by property. I am much happier with it now. The planeshapes, realmshapes, and tetrashapes are now on their own pages. Later I will add more properties of each of the shapes. Right now I only have their intersection and rolling properties. I also created a new section with formulas for the number of n-faces of n-cubes, and the n-volume of n-cubes and n-spheres.
I did a little reorganizing of the site. All of the shape related stuff is now in its own subdirectory, "shapes". Since this is a content-driven site and not a news site, I put the site map at the top of the page. I redid the round and flat side shape introduction page. It is completely rewritten and has some new images on it, so check it out even if you read it before.
I figured out how to use jar (java archive) files to put all the files for the applet into one archive file. This means that it takes a few seconds to load the applet instead of half a minute. I also made the initial location of the cubinder a little farther back on the screen so that it doesn't cover the applet initially. later i'll have its edges clipped to the viewport for the shape. Otherwise i haven't had time to do anything else. later i'll impliment shading to show distances so that it will be easier to see what the actual shapes are.
The applet that i've been working on is finally in a usable state. However, it is still in late alpha/early beta and there are still some things i want to add to it. This applet shows the projection of the cubinder plus its intersection with realmspace (3d space), and the intersections of its analogs (cylinder and circle) with the dimensions below them. I'm not sure how many browsers the applet will work for, so you might have to download the latest version of java for it to run properly. The page to view this java applet is here. I'd appreciate comments, suggestions, and bug reports on the java applet. I want to know if it was worth my time to make this and that the world actually cares :~)
Just because i don't like spam doesn't mean i don't like to get e-mail! I get
between 20 and 45 hits a day but no one makes any comments on the site. I'd like
to hear what sections you have found interesting and helpful, and which ones
are boring and useless. Also, i'd like to hear what you'd like to see more of.
If you want to contact me, you'll have to type in my e-mail manually since i don't
want any net-spiders to gather my e-mail address from my page.
The shape previously known as the 'rolosquare' on this site is now known by the name 'cubinder'. The new name is slightly more revealing about its shape and its relation to the cylinder and the four-dimensional shape called the spherinder. I have updated my subpages that make reference to it.
I added a section that tabulates the flat and curved shapes from the first to the fourth dimensions using three different methods.
I just added a section with search terms to use while searching for fourth dimension webpages. If you have any other terms of your own that you have found useful, you can contact me (see bottom) so i can put them on the page to help out others. Over the last couple of days i have been working on a java applet to help with visualizing four dimensional objects. It will show the intersections of shapes in several dimensions at once. Keep checking back :~).
For a little while I'm going to be going through this site and revising all the the sections, rewriting them and changing the terminology. Hopefully it won't take more than a couple weeks. Most of the terms that appear in the glossary aren't mentioned anywhere in the text. I will be involving those words more, plus expanding the text more so that the explanations make more sense. The pictures in the pages are a little obsolete because they use old terms, but i don't have a working scanner so i can't make new ones. Sometime later i will fix that problem.