无理
wú lǐ · HSK 7
unreasonable
无理 = 无 (without) + 理 (reason/logic) = without reason, hence unreasonable
无 means lacking or without; 理 means reason, logic, or order. Put together, 无理 literally reads as without-reason, which extends to both unreasonable behavior and an irrational number in math.
无 — top 一 + 林-like middle + fire radical 灬 below
Originally a pictograph of a person dancing while holding ornaments or tassels, meaning 'to dance' — the ancestor of 舞. It was borrowed phonetically to write the negative 'not have / without,' and the dance meaning was reassigned to 舞 with an added foot element. The simplified form 无 comes from an ancient variant.
理 — jade radical 玉/王 + village 里 (phonetic)
理 is a semantic-phonetic compound: the jade radical 王 (玉) on the left signals meaning, while 里 on the right gives the sound. It originally meant the natural veins or grain in a piece of jade, then extended to 'pattern,' 'order,' 'principle,' and finally the modern senses 'reason' and 'to manage.'