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The four square writing method is a way for teaching writing to children in school. While primarily used to teach persuasive writing , it has also been used to help teach deconstruction . [ 1 ] The method was developed by Judith S. Gould [ 2 ] and Evan Jay Gould.
Four square [1] (also called handball, champ, four squares or box ball) is a global sport played on a square court divided by two perpendicular lines into four identical boxes creating four squares labelled 1–4 or A–D. [2] Four square is a popular game at elementary schools with little required equipment, almost no setup, and short rounds ...
A four-square encipherment usually uses standard alphabets in these matrices but it is not a requirement. If this is the case, then certain words will always produce single-letter ciphertext repeats. For instance, the word MI LI TA RY will always produce the same ciphertext letter in the first and third positions regardless of the keywords used.
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Four-square cipher; Lagrange's four-square theorem, stating that any natural number equals the sum of four integers squared; Jacobi's four-square theorem giving the number of distinct ways an integer can be represented as the sum of four squares; Euler's four-square identity or theorem, the product of two numbers, each of which is a sum of four ...
Comment: The proof of Euler's four-square identity is by simple algebraic evaluation. Quaternions derive from the four-square identity, which can be written as the product of two inner products of 4-dimensional vectors, yielding again an inner product of 4-dimensional vectors: (a·a)(b·b) = (a×b)·(a×b).
In particular, for a prime number p we have the explicit formula r 4 (p) = 8(p + 1). [2] Some values of r 4 (n) occur infinitely often as r 4 (n) = r 4 (2 m n) whenever n is even. The values of r 4 (n) can be arbitrarily large: indeed, r 4 (n) is infinitely often larger than . [2]
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