d’ASH SONGS
← Back to Songs
MATH Math

The Unfinished Triangle

Original title: 未完成の三角形

Original Japanese lyrics are preserved for listening and Japanese-language practice. The explanations below are in English.

JAPAN · AGES 12–15Japan school year 2MathGeometry

送信中です

×

It might make geometry proofs a little more interesting.

LYRICS

Romaji helps you sing the Japanese words. English meaning explains them, rather than matching the tune.
Japanese wordplay and memory tricks may sound unusual in English—that’s part of the fun! The sound clues work in Japanese.
ō and ū mark long vowels (oo and uu). Original English lines are kept as written.

Hōkago no kyōshitsu yūyake ga sashikomu mado
Yuka ni nobita kage ga sukoshi zutsu kasanatte iku
“Niteru yo ne” tte waraigoe ga mada tsuzuiteru

Seikai dake ga narabu mukishitsu na kyōkasho no sumi
Onaji de aru koto o shimesu tame no
Mittsu no shirushi
Bokura wa mada sagashiteru

Mittsu no kyori ga kiseki mitai ni sorotta nara
Kono fuan mo itsuka namae o motsu no kana

Bokura ga fumidasu sentaku no anguru
Tatoe chigau michi o eranda to shite mo
Onaji mirai o sashiteru bokura no anguru

Onaji seifuku o kite onaji michi o aruite
Seikurabe mitai na kudaranai kyōsō
“Makenai yo” to waratta ano hi no mama de

Kakinagutta mama no mubōbi na nōto no sumi
Keshikasu oshinoke mitsuketai n da
San no shirushi
Bokura wa ima mo sagashiteru

Bokura no kodō ga kiseki mitai ni sorotta kara
Kono jikan ga ima tashika ni koko ni aru

Bokura ga fumidasu sentaku no anguru
Tatoe chigau michi o eranda to shite mo
Onaji mirai o sashiteru bokura no anguru

Gūzen no deai kara hajimaru
Kokoro kasanaru hitsuzen

Dakedo mada tarinai jōken
Shōmei nante mada iranai

Mittsu no kyori ga kiseki mitai ni sorotta nara
Kono jikan mo kitto imi o motsu

Bokura ga fumidasu sentaku no anguru
Tatoe chigau michi o eranda to shite mo
Onaji mirai o sashiteru bokura no anguru

Bokura wa mada kasanarikire nai
Mikansei no sankakukei

Mikansei no sankakukei

What can you discover in this song?

What marks might the song be looking for?

LYRIC SHEET

Download the lyrics and look a little deeper.

The word “angle” appears several times in this song.
What part of mathematics might it connect with?

Once you notice the connection, the song may sound a little different.

DISCOVER SONGS

Explore a little further from this song.