Hei tauira, i whakakapihia e Arnold Sommerfeld (1910) te tohu a Minkowski ki te tohu vector ataahua, ka hangaia nga kupu "wha vector" me te "ono vector". I whakauruhia e ia he whakatakotoranga trigonometric o te ture taapiri tere, e ai ki a Sommerfeld, ka whakakore i te nuinga o te maere o taua kaupapa. Ko etahi atu takoha nui i mahia e Laue (1911, 1913), nana i whakamahi te whakatakotoranga waahi-waahi ki te hanga i tetahi ariā whanaunga o nga tinana whakakorekore me te ariā matūriki. I whakarahihia e ia nga korero a Minkowski mo nga mahinga hiko hiko ki nga kaha katoa ka whakamarama i te kaupapa o te taurite-hinengaro.
he whakatakotoranga trigonometric o te ture taapiri tere