Suugaku - What is Japanese mathematics like?

Many people end up wondering how mathematics works in Japan, because the writing system looks so different from the Western one. Mathematics in Japanese is called suugaku (数学), and Japanese history names two kinds of it: the Western tradition is called yousan (洋算) and the Japanese way is wasan (和算). Japanese also has its own numbers using ideograms, but they also use Western numbers. Japanese numbers and counting are much more logical and systematic than Western ones. We recommend that you already have knowledge about Japanese numbers so you don't get lost in Japanese mathematics.

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Wasan - The mathematical origin in Japan

Wasan was developed in Japan during the Edo period (1603-1867). The term wasan literally means Japanese (和) calculation (算). It was coined in the 1870s to distinguish that tradition from Western mathematics, and it faded from school arithmetic after Meiji Japan adopted yousan. In the classroom today there are not many differences: the signs and the operations are the same as in the West. Wasan remains the historical Japanese tradition, with its own books, tools, and temple tablets. Among the history of mathematics in Japan, one of the best-known inventions is the soroban, the Japanese abacus. There is also sangaku: wooden tablets with mathematical problems, often geometry, that were dedicated at temples and shrines. Seki Takakazu (関孝和), also called Seki Kowa, was the most influential wasan mathematician of the Edo period. He developed methods for solving systems of linear equations by eliminating unknown variables.

Multiplication trick

There is a visual method, often called Japanese multiplication on the internet, that makes some products easier to see. It consists of drawing sets of parallel lines that represent each digit of the first number to be multiplied. Then draw sets of parallels, perpendicular to the first sets of parallels, corresponding to each digit of the second number (the multiplier). Look at the figure and count the number of intersections of the parallel lines: I can't explain well in words, but each alignment of the parallel lines represents a digit of the final result. And just like in traditional multiplication, it is better to obtain the result by counting the numbers starting from the back. See one of the examples in the figure written in calculations to see how this method is simpler than the traditional one: 23 x 12 = (2x10 + 3)(1x10 + 2) = 2x1x10² + [2x2x10 + 3x1x10] + 3x2 = 276

How do the Japanese do calculations?

Mathematics in Japan is done the same way as in the West. Japanese children are introduced to the Arabic numbers we use, and they also keep the kanji numerals. One of the few things that changes is the pronunciation in Japanese; if you know English, the loanwords such as plus and minus are easy to recognize. We use the same mathematical signs from Western mathematics in Japanese. Japanese also uses the verbs to add, multiply, and the rest, together with kanji. We use tasu (足す) as the verb for addition, to sum or more. Example: 7 + 3 = 10 / nana tasu san wa juu desu (七足す三は十です). The result is often marked with wa (は), and the sentence can close with desu (です): X + Y は 50 です。 The word ten (点) is the decimal point. Example: 3.5 (san ten go). The four operations together are called kagenjojo (加減乗除). In speech you also hear English-derived words such as plus and minus. Below we will see a list of their pronunciation:

	Japanese	Derived from English
Addition / plus	tasu (足す)	purasu (プラス)
Subtraction / minus	hiku (引く)	mainasu (マイナス)
Multiplication / times	kakeru (掛ける)
Division / divided	waru (割る)
Fractions	bun (分)

The verbs for adding, subtracting, multiplying, and dividing followed by zan (算) are used to say addition, subtraction, multiplication, and division: 足し算 (tashizan), 引き算 (hikizan), 掛け算 (kakezan), 割り算 (warizan).

Mathematical vocabulary in Japanese

Of course, this is just the basics about mathematics in Japanese. For you to delve deeper, we will leave a vocabulary table for you to conduct your research:

English	Japanese	Romaji
Mathematics	数学	suugaku
Number	数字 / 数	suuji / kazu
Digit	桁	keta
Decimal	小数	shousuu
Fraction	分数	bunsuu
Divisor	約数	yakusuu
Exponent	指数	shisuu
Even number	偶数	guusuu
Odd number	奇数	kisuu
Irrational number	無理数	murisuu
Rational number	有理数	yuurisuu
Ratio	比	hi
Quantity	量	ryou
Volume	体積	taiseki
Area	面積	menseki
Angle	角度	kakudo
Length	長さ	nagasa
Weight	重さ	omosa
Speed	速さ	hayasa
Prime number	素数	sosuu
Negative number	負の数	fu no suu
Positive number	正の数	sei no suu
Calculus	微積分学	bisekibungaku
Differential calculus	微分学	bibungaku
Integral calculus	積分学	sekibungaku
Multivariable calculus	多変数微分積分学	tahensuubibunsekibungaku
Trigonometry	三角法	sankakuhou
Probability	確率	kakuritsu
Statistics	統計	toukei
Geometry	幾何学	kikagaku
Algebra	代数学	daisugaku
Linear Algebra	線型代数学	senkeidaisuugaku
Differential Geometry	微分幾何学	bibunkikagaku
Square	正方形	seihoukei
Triangle	三角形	sankakukei
Rectangle	長方形	chouhoukei
Trapezium	台形	daikei
Parallelogram	平行四辺形	heikoushihenkei
Rhombus	菱形	hishigata
Kite	凧形	takogata
Cube	立方体	rippoutai
Pyramid	角錐	kakusui
Square Pyramid	四角錐	shikakusui
Prism	角柱	kakuchuu
Triangular Prism	三角柱	sankakuchuu

With the names above you can read a Japanese textbook page or a classroom explanation without guessing from the symbols alone. Start with tasu, hiku, kakeru, and waru, then come back to the table when a page throws an unfamiliar kanji at you.