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The monad puzzle

Puzzle

The sign of the great Monad, which was unwittingly adopted as its seal by the Northern Pacific Railway Company, means to a Chinaman exactly what the cross does to a Christian. It is the sign of Deity, and represents eternity,—the everlasting, as Chinese scholars express it,—and is to-day an object of veneration to over 400,000,000 people. It was adopted by the Northern Pacific Railway Company as a seal and trade-mark at the time of the organization of the company, and appears on all of its freight cars, bonds, stock certificates and advertisements, and it is familiar to everyone who has occasion to use the timetables.

It was adopted at the suggestion of Chief Henry McHenry, who says he had no conception of its Chinese significance, but merely intended it to represent certain mathematical proportions. This fact I have only just learned, so it will be interesting to know how far Mr. McHenry's views coincide with my own as given in the puzzle connected with it. The best thing I ever heard about the sign was told to me by P. H. Tighe, the famous manufacturer of base balls, who got the idea of the two-piece cover from the shape of the monad.

Attention was first called to the significance of the symbol by Rev. W.S. Holt, who is a thorough Chinese scholar, and is familiar with its meaning through his connection with Chinese missions. Several works have been written on the symbol which prove its great antiquity, and in them are given the various interpretations which oriental scholarshave put upon it. As a rule, these explanations are so mixed up with oriental theology, such, for instance, as the Yin and Yan, the male and female forces of nature, and "the illimitable as adverse to the great extreme," that the reader feels as if he were investigating the Keely motor.

One writer on the subject is of the opinion that the sign has some recondite mathematical significance, and quotes ancient Chinese works as saying: "The illimitable produces the great extreme. The great extreme produces the two principles. The two principles produce the four quarters, and from the four figures we develop the quadrature of the eight diagrams of Feuh-hi." This was written more than three thousand years ago, and yet, so far as I can learn, has never been connected with the mathematical "squaring of the circle," although it looks very much like it, and is suggestive of the following propositions: —The first proposition is given as a simple puzzle for young folks. With one continuous line, divide the black and white parts of the Monad (the Yin and the Yan), into four pieces of the same shape and size.

The second proposition is to divide by one straight cut the Yin and the Yan, (supposing them to be two pieces already,) each into two pieces of the same size. This can also be done by those without any great mathematical ability.

The third proposition is to prove the "affinity" between the Monad and the "good-luck" sign, by converting the two horseshoes, as shown in Figures 1 and 3, into a perfect Monad, in the shortest possible way.

Puzzle in short

1. With one continuous line, divide the black and white parts of the Monad (the Yin and the Yan), into four pieces of the same shape and size.
2. Divide by one straight cut the Yin and the Yan, (supposing them to be two pieces already,) each into two pieces of the same size.
3. Prove the "affinity" between the Monad and the "good-luck" sign, by converting the two horseshoes into a perfect Monad