Tātai arotahi kōpiko

I mua i te whakatakoto i te tātai mō te karu arotahi kōpiko, kia mārama tuatahi ki ētahi ture mō ngā tohu o te karu arotahi kōpiko.

Ture Tohu Arotahi Kōpiko
- Te tawhiti o te mea
Mena kei te taha kotahi o te karāhe te mea me te ahunga e puta mai ana te hihi mārama, kātahi tawhiti o te mea kua tohua he pai.
- Te tawhiti o te ahua (s')
Ki te puta he hihi mārama mā roto i te atarangi, kātahi tawhiti atarangi kua tohua he pai (ahua tūturu). Ki te kore te ahua e tukuna e te hihi mārama, kātahi ka tawhiti atarangi tohu kino (ahua mariko).
- Roanga arotahi (f)
Ina tukuna te pūwāhi arotahi o te karu arotahi mā roto i te hihi mārama, kātahi ka roa arotahi Kua tohua te arotahi he pai. I tetahi atu taha, ki te kore te hihi mārama e whiti i te pūwāhi arotahi o te arotahi, kāti roa arotahi Kua tohua te arotahi he kino. Kāore te hihi mārama e whiti i te pūwāhi arotahi o te arotahi kōpiko nā tēnei. roa arotahi he kino te karu arotahi kōpiko.
- Teitei o te mea (h)
Mena kei runga ake te mea i te tuaka o te karu kōpiko, kāti te teitei o te mea tohu pai (mea poutū). I tetahi atu taha, ki te mea kei raro iho te mea i te tuaka o te karu whāiti, kāti te teitei o te mea tohu kino (mea huripokitia).
- Teitei o te atarangi (h')
Mena kei runga ake te ahua i te tuaka o te karu kōpiko, kāti teitei o te atarangi tohu pai (ahua poutū). Mena kei raro iho te ahua i te tuaka o te karu kōpiko, kātahi teitei o te atarangi tohu kino (ahua huripokitia).
- Whakanui whakaahua (m)
Mena he nui ake te whakanui o te ahua i te 1, he nui ake te rahi o te ahua i te rahi o te mea. Mena he 1 te whakanui o te ahua, he rite tonu te rahi o te ahua ki te rahi o te mea. Mena he iti ake te whakanui o te ahua i te 1, he iti iho te rahi o te ahua i te rahi o te mea.
 
Tātai Arotahi Kōpiko
Tirohia te ahua i raro nei. E rua ngā hihi mārama e whakaaturia ana e anga atu ana ki tētahi karāhe kōpiko, kātahi ka hurihia ngā hihi mārama e te karāhe kōpiko.

Taitara:
s = tawhiti o te mea, s' = tawhiti o te ahua, h = P P' = teitei o te mea, h' = Q Q' = teitei o te ahua, F₁ me F₂ = te pūwāhi arotahi o te karu arotahi kōpiko.

I roto i te hihi mārama P'AS, he rite te tapatoru P'AP ki te tapatoru Q'AQ. Nō reira:
I roto i te hihi mārama P'BR, te tapatoru BF₂He rite a A ki te tapatoru Q'F₂Q ko te tawhiti AB = te teitei o te mea (h) me te tawhiti F₂A = te roa arotahi (f) o te arotahi kōpiko. Pēnei:
He ōrite ngā taha maui me ngā taha matau o ngā whārite 1 me te 2, nō reira ka ōrite ngā taha matau:
Whakareatia ngā taha e rua o te whārite ki te s' :
I runga anō i ngā ture o te tohu karu kōpiko, ka taea te whakarerekē i tēnei tātai kia pēnei: tātai whakaata piko, Ki te mea tawhiti o te ahua (s') ka hoatu he tohu kino nā te mea kāore te atarangi e whiti ana i te hihi mārama, ā, roa arotahi (f) ka hoatu hoki he tohu kino nā te mea kāore te pūwāhi arotahi o te karu kōpiko e tukuna e te mārama (whakatairite ki te ahua o te hanganga o te ahua i runga ake nei). E ai ki tēnei kōrero, ka huri te tātai mō te karu kōpiko i runga ake nei ki:
Whakaahuatanga: s = tawhiti o te mea, s' = tawhiti o te ahua, f = roa o te arotahi.
Kia maumahara tonu ki te ture tohu arotahi kōpiko ina whakamahia ana tēnei tātai hei whakaoti rapanga arotahi kōpiko.

Whakanui Whakaahua (m)
Mātakihia te ahua o te hanganga o te atarangi o te mea i runga ake nei. He rite tonu ngā tapatoru P'AP me Q'AQ, nō reira ka taea e tātou te whakatau i te whanaungatanga i waenga i te tawhiti o te mea me te tawhiti atarangi me te teitei o te mea me te teitei o te atarangi:
Ka tuhia anō tēnei tātai penei i raro nei mā te tāpiri i te m:
Ngā Mōhiohio:
m = te whakanui o te ahua
h = te teitei o te mea (he pai mēnā kei runga ake i te tuaka o te karāhe kōpiko, o te mea poutū rānei)
h' = te teitei o te ahua (pai mēnā kei runga ake i te tuaka o te karāhe kōpiko, kei te poutū rānei te ahua)
s = tawhiti o te mea (pai mēnā ka hipa te mea hihi mārama e haere mai ana)
s' = tawhiti o te ahua (pai mēnā ka tukuna te ahua mā roto) hihi mārama te ahua tūturu rānei)
 
Ngā Tauira Pātai mō ngā Arotahi Kōpiko
Ako tauira o te karu arotahi kōpiko kia pai ake ai tō mārama ki te whakamahi i te tauira karāhe kōpiko.

Ngā Pātai Whakaharatau mō ngā Arotahi Kōpiko
Meatia ngā pātai whakaharatau mō ngā karāhe kōpiko kia matatau ake ai koe ki te whakaoti rapanga karāhe kōpiko.