Clock angle problem

thumb|Eserese a na-egosi akụkụ ndị a kpụrụ n'aka nke elekere analọg na-egosi oge nke 2:20
Nsogbu akụkụ elekere bụ ụdị nsogbu mgbakọ na mwepụ nke gụnyere ịchọta akụkụ n'etiti aka elekere analọg.

## Nsogbu mgbakọ na mwepụ
Nsogbu n'akuku elekere na-ejikọta nha abụọ dị iche iche: akụkụ na oge.  A na-atụkarị akụkụ ahụ na ogo site na akara nke nọmba 12 n'akụkụ elekere.  Oge na-adaberekarị na elekere elekere iri na abụọ.

Usoro iji dozie nsogbu ndị dị otú ahụ bụ ịtụle ọnụego mgbanwe nke akụkụ na ogo kwa nkeji.  Aka elekere nke elekere analọgụ elekere 12 nkịtị na-atụgharị 360° n'ime awa iri na abụọ (nkeji 720) ma ọ bụ 0.5° kwa nkeji. Aka nkeji -na-atụgharị site na 360° na nkeji 60 ma ọ bụ 6° kwa nkeji

### Nhazi maka akụkụ nke aka elekere

: \theta_{\text{hr}} = 0.5^{\circ} \times  M_{\Sigma} = 0.5^{\circ} \times (60 \times H + M)

ebe:

* θ bụ akụkụ dị n'ogo nke aka a tụrụ n'akụkụ elekere site na 12
* H bụ oge.
* M bụ nkeji gafere awa.
* MΣ bụ ọnụọgụ nkeji kemgbe elekere iri na abụọ.        M    Σ     = (60 × H + M)      {\displaystyle M_{\Sigma }= (60\oge H+M) } 

 M_{\Sigma} = (60 \times H + M)

### Njikọ maka akụkụ nke aka nkeji

: \theta_{\text{min.}} = 6^{\circ} \times M

ebe:

* θ bụ akụkụ dị n'ogo nke aka a tụrụ ya na elekere site na ọnọdụ elekere iri na abụọ.
* M bụ nkeji.

#### Ihe Nlereanya
Oge bụ 5:24. Akụkụ na ogo nke aka awa bụ:

: \theta_{\text{hr}} = 0.5^{\circ} \times  (60 \times 5 + 24) = 162^{\circ}

Akụkụ na ogo nke aka nkeji bụ:

: \theta_{\text{min.}} = 6^{\circ} \times 24 = 144^{\circ}

### Njikọ maka akụkụ dị n'etiti aka
Enwere ike ịchọta akụkụ dị n'etiti aka site na iji usoro a:

: \begin{align}
\Delta\theta
 &= \vert \theta_{\text{hr}} - \theta_{\text{min.}} \vert \\
 &= \vert 0.5^{\circ}\times(60\times H+M) -6^{\circ}\times M \vert \\
 &= \vert 0.5^{\circ}\times(60\times H+M) -0.5^{\circ}\times 12 \times M \vert \\
 &= \vert 0.5^{\circ}\times(60\times H -11 \times M) \vert \\
\end{align}

ebe

* H bụ oge
* M bụ nkeji

Ọ bụrụ na oghere ahụ karịrị ogo 180 wee wepụ ya na ogo 360.

#### Ihe ọmụmaatụ  1
Oge bụ 2:20.

: \begin{align}
\Delta\theta 
 &= \vert 0.5^{\circ} \times (60 \times 2 - 11 \times 20) \vert \\
 &= \vert 0.5^{\circ} \times (120 - 220) \vert \\
 &= 50^{\circ}
\end{align}

#### Ihe ọmụmaatụ 2
Oge ahụ bụ 10:16.

: \begin{align}
\Delta\theta 
 &= \vert 0.5^{\circ} \times (60 \times 10 - 11 \times 16) \vert \\
 &= \vert 0.5^{\circ} \times (600 - 176) \vert \\
 &= 212^{\circ} \ \ ( > 180^{\circ})\\
 &= 360^{\circ} - 212^{\circ} \\
 &= 148^{\circ}
\end{align}

### Kedu mgbe a na-atụkwasị aka elekere na nkeji?
[thumb|300x300px|Na ngwọ''T'' eserese a, T na-egosi oge n'ime awa; ''P'', ọnọdụ aka; na ''θ'', akụkụ aka na ogo. Ahịrị na-acha uhie uhie (nke siri ike) na-egosi aka awa; ahịrị na- acha anụnụ anụnụ (nke siri ezigbo ike) na na-egosi obere aka. Nkwekọrịta ha (red square) bụ mgbe ha kwụ n'ahịrị. Na mgbakwunye, okirikiri oroma (ahịrị dash-dot) bụ mgbe aka na-emegide, na triangles pink (akara dashed) bụ mgbe ha kwụ ọtọ.Na [http://upload.wikimedia.org/wikipedia/commons/1/1a/Clock_angle_problem_graph.svg faịlụ SVG&nbsp;&nbsp;], na-efegharị n'elu eserese iji gosipụta ọnọdụ aka n'ihu elekere.](https://ig.wikipedia.org/wiki/Us%C3%B2r%C3%B2:Clock_angle_problem_graph.svg)
A na-etinye aka awa na nkeji naanị mgbe akụkụ ha bụ otu.

: \begin{align}
\theta_{\text{min}} &= \theta_{\text{hr}}\\
\Rightarrow 6^{\circ} \times M &= 0.5^{\circ} \times (60 \times H + M) \\
\Rightarrow 12 \times M &= 60 \times H + M \\
\Rightarrow 11 \times M &= 60 \times H\\
\Rightarrow M &= \frac{60}{11} \times H\\
\Rightarrow M &= 5.\overline{45} \times H
\end{align}

 is an integer in the range 0–11. This gives times of: 0:00, 1:05., 2:10., 3:16., 4:21., 5:27.. 6:32.,  7:38., 8:43., 9:49., 
10:54., and 12:00.
(0. minutes are exactly 27. seconds.)

## Hụkwa Ihe Ọzọ

* Ebe elekere dị

## Edensibia

## Njikọ mpụga

* https://web.archive.org/web/20100615083701/http://delphiforfun.org/Programs/clock_angle.htm
* http://www.ldlewis.com/hospital_clock/ - nyocha dị ukwuu nke akụkụ elekere
* https://web.archive.org/web/20100608044951/http://www.jimloy.com/puzz/clock1.htm