Whakaoti i te 1/alpha-1=1/2pi

$$\frac { 1 } { \alpha - 1 } = \frac { 1 } { 2 \pi }$$

Whakaoti mō α

$$\alpha =2\pi +1\approx 7.283185307$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe \alpha ki 1 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te \alpha -1.

$$1=\frac{1}{2}\left(\alpha -1\right)\pi ^{-1}$$

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{1}{2} ki te \alpha -1.

$$1=\left(\frac{1}{2}\alpha -\frac{1}{2}\right)\pi ^{-1}$$

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{1}{2}\alpha -\frac{1}{2} ki te \pi ^{-1}.

$$1=\frac{1}{2}\alpha \pi ^{-1}-\frac{1}{2}\pi ^{-1}$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$\frac{1}{2}\alpha \pi ^{-1}-\frac{1}{2}\pi ^{-1}=1$$

Me tāpiri te \frac{1}{2}\pi ^{-1} ki ngā taha e rua.

$$\frac{1}{2}\alpha \pi ^{-1}=1+\frac{1}{2}\pi ^{-1}$$

Whakaraupapatia anō ngā kīanga tau.

$$\frac{1}{2}\times \frac{1}{\pi }\alpha =\frac{1}{2}\times \frac{1}{\pi }+1$$

Me whakarea te \frac{1}{2} ki te \frac{1}{\pi } mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{1}{2\pi }\alpha =\frac{1}{2}\times \frac{1}{\pi }+1$$

Tuhia te \frac{1}{2\pi }\alpha hei hautanga kotahi.

$$\frac{\alpha }{2\pi }=\frac{1}{2}\times \frac{1}{\pi }+1$$

Me whakarea te \frac{1}{2} ki te \frac{1}{\pi } mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{\alpha }{2\pi }=\frac{1}{2\pi }+1$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia 1 ki te \frac{2\pi }{2\pi }.

$$\frac{\alpha }{2\pi }=\frac{1}{2\pi }+\frac{2\pi }{2\pi }$$

Tā te mea he rite te tauraro o \frac{1}{2\pi } me \frac{2\pi }{2\pi }, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{\alpha }{2\pi }=\frac{1+2\pi }{2\pi }$$

He hanga arowhānui tō te whārite.

$$\frac{1}{2\pi }\alpha =\frac{2\pi +1}{2\pi }$$

Whakawehea ngā taha e rua ki te \frac{1}{2}\pi ^{-1}.

$$\frac{\frac{1}{2\pi }\alpha \times 2\pi }{1}=\frac{2\pi +1}{2\pi \times \frac{1}{2\pi }}$$

Mā te whakawehe ki te \frac{1}{2}\pi ^{-1} ka wetekia te whakareanga ki te \frac{1}{2}\pi ^{-1}.

$$\alpha =\frac{2\pi +1}{2\pi \times \frac{1}{2\pi }}$$

Whakawehe \frac{1+2\pi }{2\pi } ki te \frac{1}{2}\pi ^{-1}.

$$\alpha =2\pi +1$$

Tē taea kia ōrite te tāupe \alpha ki 1.

$$\alpha =2\pi +1\text{, }\alpha \neq 1$$