Map Projections

These pages describe a number of well-known map projections, and how they are drawn and used. I also include a map projection I designed while at University, circa 1978. It is a conventional projection, neither conformal nor equal-area, which depicts the world on an ellipse with a 3:2 aspect ratio.

Other Topics

Telescopes and eyepieces: a short page explaining how a telescope works, and describing various common types of telescopes and eyepieces.

HTML: A brief summary of HTML, to help you to write your own web page, was added, since this site contains lots of examples, and was created with a text editor (and hence its HTML source code is nice and readable).

Colors: This page contains a couple of pretty color charts. May not display perfectly in 256-color mode.

Signal Flag Systems: This page contains a picture showing the flags used for the International Code of Signals, as used by ships, and the flags from some other signalling systems as well.

An example of a computer architecture, which illustrates how computers work at the machine language level.

A brief discussion of my thoughts on a computer language that is mostly an improved FORTRAN.

Illustrations of a few designs for computer keyboards that have been used through the ages.

And some comments on why I favor big-endian architecture, and how I wish text files should be stored.

Chess: here, I suggest a new approach to explaining some of the rules of chess that confuse beginners, and I propose an extremely modest rule change to chess that might help to improve its interest and popularity without changing it so much as to, in essence, replace it by another game.

The Musical Scale: here, I briefly discuss the integer harmonic ratios that have given rise to the scale used in Western music.

A Space Habitat Design: The problem of secondary radiation from cosmic rays has been claimed to make space habitats, such as those envisaged by Gerard K. O'Neill, impractical. Here is illustrated a design, admittedly less exciting in appearance than designs with large expanses of glass open to space, that can work even if one needs six metres of rock for shielding. The shielding doesn't rotate, so large structural loads are avoided, and consumables are not required to re-orient the structure to the sun on a continuing basis.

Travelling to Mars: I briefly discuss some of the things involved in sending people to Mars, describing the Hohmann orbit, and Dr. Zubrin's Mars Direct proposal and NASA's Mars Reference Mission derived from it.

Lining up the Planets: a brief look at how often the planets line up in a row.

A Tall Building Design: a conventional idea for how a tall building might be made, inspired by the recent construction of many tall buildings around the world.

Movie and TV Aspect Ratios: a field guide to the "black bars" you may see on a TV set when watching widescreen movies in their original form.

A Limitation of Color Photography: I note that color photography, as ordinarily carried out with film, has an intrinsic limitation as regards the control of contrast, and illustrate that it can be solved, and the benefit of doing so.

Some unit conversions are on this page, mostly for printing and page layout.


Pentagonal Tilings: Here is a page filled with pretty pictures, of a tiling of the plane with pentagons and a few other shapes.

Slide Rules: I explain how a slide rule works, even showing what the log-log scales were for.

Infinity: This page tries to explain some topics that are often confusing to nonmathematicians, primarily the Cantorian theory of transfinite numbers.

Archimedian Solids: This page discusses the three-dimensional solids which are the next step in complexity after the Platonic solids.

The Fourth Dimension: This page discusses the five three-dimensional Platonic solids, shows an illustration of the hypercube, and briefly describes the other four-dimensional regular object. But it does have one excuse for existing: a diagram which may make it clearer how the dodecahedral faces of the 120-cell are connected to each other.

Dodecahedral Rotations: This page contains a diagram of the possible rotations of a dodecahedron, showing the symmetry involved (which is also that of the A5 alternating group).

Probability: A small page about probability, featuring the odds at Hazard.

Groups, Rings, and Fields: some unusual groups are illustrated on this page.

Sphere Packing: On this page, I include some diagrams of the face-centered cubic packing of spheres, as well as packings of circles in two dimensions, and I also include a diagram illustrating the E8 packing of hyperspheres in eight dimensions.

Gödel's Proof and the Halting Problem: this page describes these two related profound proofs of the limits to mathematics.

Two Famous Equations: Two equations due to Euler are explained here, along with much of mathematics.

Euler's Constant is described on another page.

Magic Squares: An example of a bimagic square, and the simple rules for constructing magic squares of some orders.


The Einstein-Podolsky-Rosen experiments: This page tries to explain the apparent paradox, proven to be real by experiment, which seems to indicate that in quantum mechanics there are things that move faster than the speed of light.

And on another page, I explain what the mysterious fine-structure constant is, the reciprocal of which, approximately 137.036, has fascinated many.


On another page, I discuss the controversial theory of Punctuated Equilibria originated by Stephen Jay Gould and Niles Eldredge.


Perpetual Calendars: This page gives perpetual calendars for the Julian and Gregorian systems, for the seven-day week and for 10- and 12- day weeks to allow the position of a day within the Chinese sexagesimal cycle to be found.

A Luni-Solar Calendar: This page has an involved proposal for a calendar that is geared to both the mean tropical year and the mean synodic month, which only loses .007 days in 30,000 years.

A Simplified Calendar: This page contains an alternative proposal for a calendar that is uniform from year to year, without disrupting the continuity of the week, important in many religious faiths.

Finding the Julian Day: This page deals with converting from the Gregorian and Julian calendars to Julian Day Numbers.

A Martian Calendar: This page discusses how timekeeping might be done on Mars, and it also has a link to a page where the subject is handled in more detail.

A Unified Architecture for Telephone Numbers: a modest proposal for returning to the civilized days of seven-number dialing instead of ten-number dialing whenever possible.

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Copyright (c) 1998, 1999, 2000, 2001 John J. G. Savard