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Kwati a Wɔkwati Trigonometry (2013) .

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14 min read Via iquilezles.org

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Honhom a Ɛwɔ Afiri no Mu: Dɛn na Na Ɛrekwati Trigonometry (2013)?

Wɔ afe 2013 mu no, adeyɛ bi a ɛyɛ nwonwa gyee ntini wɔ wiase a wɔyɛ softwea. Blog asɛm bi a wɔato din "Avoiding Trigonometry" a programmer Maciej Cegłowski kyerɛwee no gyee mfiridwumayɛfo a wɔwɔ baabiara adwene. Na ɛnyɛ sine ne cosine a ɛyɛ den no ho asɛm, na mmom na ɛfa ɔhaw bi a ɛyɛ anifere kɛse ho: mfiridwuma mu ɛka. Cegłowski kaa ne suahu a ɔde siesiee bɔne bi a ɛnyɛ den wɔ imageboard site a agye din, 4chan no mu kɔɔ akyiri. Ɔdebɔneyɛfo no? Nhyehyɛe a ɛyɛ nwonwa a ɛyɛ ntanta, a wɔayɛ no boro so a wɔde di mfonini a ɛkyinkyini ho dwuma a na ɛde ne ho to nkɔnsɔnkɔnsɔn a ɛyɛ nwonwa a ɛyɛ server-side trigonometry akontaabu so. Na nkrasɛm titiriw no mu dɔ: na wɔn a wɔyɛe no abɔ mmɔden kɛse ayɛ Rube Goldberg afiri bi de akwati ano aduru a ɛnyɛ den na ɛyɛ fɛ a wobetumi anya ntɛm wɔ nnɛyi wɛb brawsa ahorow mu. Saa asɛm yi bɛyɛɛ nhwɛsoɔ a ɛyɛ canonical a ɛkyerɛ sɛdeɛ mfiridwuma a ɛboro soɔ ma ɛyɛ mmerɛw, sɛe nneɛma, na awieeɛ koraa no ɛma nkɔsoɔ brɛ ase kɔ crawl.

Anifere Ho Ka Kɛse

"Avoiding Trigonometry" asɛm no yɛ masterclass wɔ nea efi nyansa a wɔmfa nni dwuma yiye mu ba no mu. Akyinnye biara nni ho sɛ na wɔn a wɔyɛɛ mfitiase nhyehyɛe no ho akokwaw. Wɔde ano aduru a ɛyɛ den dii ɔhaw bi a emu yɛ den ho dwuma. Nanso, wɔn "anifere" mmara no de adesoa a ɛtra hɔ kyɛ bae. Na ɛsɛ sɛ nsakrae biara, mfomso biara a wosiesie, ne ade foforo biara fa saa ntease a ɛyɛ nwonwa yi mu. Bere a mfiase no wɔkoraa so denam ɔkwan a ɛyɛ mmerɛw a wɔanyɛ ho nhwehwɛmu so no, nnɔnhwerew mpempem pii a wɔde hwɛɛ nhyehyɛe a ɛyɛ den no so na wɔyɛɛ ho adwuma no yɛɛ ketewaa. Eyi ne mfiridwuma mu ɛka titiriw —ɛyɛ mfɛntom a wotua wɔ ɔkwan tiawa bi so a na ɛnsɛ sɛ wɔfa da. Wɔ nnɛyi nnwuma fam no, eyi kyerɛ tẽẽ kɔ bere a wɔde kɔ gua so brɛoo ma nneɛma foforo, nkɔso akuw a wɔn abam abu, ne codebase a ɛbɛyɛ asiane na ne bo yɛ den sɛ wɔbɛsesa.

  • Agility a wɔatew so: Ɛyɛ den sɛ wɔbɛsesa nhyehyɛe a ɛyɛ den. Nea ɛsɛ sɛ ɛyɛ update a ɛnyɛ den no bɛyɛ adwuma kɛse, a ɛmma adwuma no ntumi nsakra ntɛmntɛm.
  • Mfomso Mpɛn dodow a ɛkɔ soro: Nneɛma a ɛyɛ den kɛse kyerɛ sɛ nsɛntitiriw pii a ebetumi ama adi nkogu. Sɛ wosiesie mfomso biako a, ebetumi ama woanya abien foforo a wunhyɛ da.
  • Nimdeɛ Silos: Mfitiaseɛ nnwumayɛfoɔ kakraa bi pɛ na wɔbɛtumi ate nteaseɛ a ɛyɛ ntanta no ase, na ɛde nsɛnnennen ne adwumayɛ mu asiane bɛba.
  • Demoralized Developers: Mfiridwumayɛfo a wɔwɔ nimdeɛ mpɛ sɛ wɔbɛyɛ nsiesie adwumayɛfo ama brittle code; wɔpɛ sɛ wɔkyekye ano aduru foforo.

Fapem a Wɔbɛkyekyere a Ɛko Tia Nneɛma a Ɛyɛ Den

Enti, ɛbɛyɛ dɛn na nnwuma atumi akwati wɔn ankasa "Avoiding Trigonometry" no? Mmuae no gyina sɛnea wɔde nneɛma a ɛyɛ mmerɛw ne nea emu da hɔ bedi kan afi mfiase no so. Eyi kyerɛ sɛ wɔbɛkyekyere nhyehyɛe ahorow a ɛhyɛ adansi a ɛho tew na ɛyɛ modular ho nkuran. Ɔkwan a wɔfa so yɛ modular hyɛ nteɛso denam nneɛma a ɛyɛ den a ɛpaapae mu yɛ no nneɛma nketenkete a wotumi di ho dwuma, na wotumi sesa so. Sɛ afã biara wɔ asɛyɛde biako a wɔakyerɛkyerɛ mu yiye a, ɛbɛyɛ mmerɛw sɛ wɔbɛte nhyehyɛe no nyinaa ase, asɔ ahwɛ, na wɔayɛ nsakrae. Eyi ne nyansapɛ a ɛwɔ nnɛyi nhyiam ase a wɔayɛ sɛ ɛbɛma adwumayɛ ayɛ mmerɛw akyi. Sɛ nhwɛsoɔ no, Mewayz de modular adwumayɛ OS a ɛboa nnwumakuo ma wɔkwati sɛ wɔbɛkyekyere nhyehyɛeɛ a ɛyɛ ntanta, a ɛka bom. Ɛdenam module soronko a ɔde ma CRM, adwuma no sohwɛ, ne nkitahodi a ɛka bom a ɛho tew so no, Mewayz hwɛ hu sɛ nsɛm a ɛyɛ den no ahyɛ mu, na ɛnyɛ nea ɛyɛ kɛse.

"Ɛsɛ sɛ saa trigonometry koodu no ho ka nyinaa, a nnɔnhwerew a mede yii no ka ho no, kɔ dɔla ɔpehaha pii. Ne nyinaa ne sɛ wɔbɛkwati dapɛn awiei adwuma a ɛsom bo a ɛbɛma mfonini a wɔdannan no asi wɔ akraman no so." - Maciej Cegłowski, "Wɔkwati Trigonometry" (2013)

Efi Mfiridwuma mu Basabasayɛ so kosi Adwumayɛ mu pefeeyɛ so

Asuade a ɛne "Avoiding Trigonometry" no trɛw kɔ akyiri sen server dan no. Ɛyɛ bɛ ma adwuma bi afã horow nyinaa. Sɛ́ ɛyɛ byzantine pene nhyehyɛe, softwea nnwinnade a wɔatwa mu a wɔabɔ no asinasin, anaasɛ dwumadibea nkitahodi kwan a ɛde ne ho to "abusuakuw nimdeɛ" so no, saa nsɛm a ɛyɛ den yi yɛ adwumayɛ a ɛne saa mmara a ɛyɛ tan no yɛ pɛ. Wɔma akasakasa ba, ɛma gyinaesi yɛ brɛoo, na wɔmma ahyehyɛde no ntumi nyɛ adwuma sɛ ade mũ a ɛka bom. Ɛsɛ sɛ botae no yɛ sɛ wɔbɛbɔ nhyehyɛe ahorow—mfiridwuma ne akwan a wɔfa so yɛ adwuma nyinaa—a ɛyɛ mmerɛw na ɛyɛ mmerɛw sɛnea wobetumi. Ɛnam sɛ wɔpaw nhyiamu a ɛsi nkabom ne pefeeyɛ so dua, te sɛ Mewayz so no, nnwuma bɛtumi ahwɛ sɛ wɔn adwumayɛ fapem no ma nkɔsoɔ tumi mmom sen sɛ ɛbɛsiw kwan. Wobetumi de wɔn ahoɔden adi dwuma de akɔ wɔn anim, sen sɛ wɔbɛkyerɛkyerɛ gyinaesi ahorow a ɛyɛ ntanta a atwam no mu bere nyinaa.

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Nsɛmmisa a Wɔtaa Bisa

Honhom a Ɛwɔ Afiri no Mu: Dɛn na Na Ɛrekwati Trigonometry (2013)?

Wɔ afe 2013 mu no, adeyɛ bi a ɛyɛ nwonwa gyee ntini wɔ wiase a wɔyɛ softwea. Blog asɛm bi a wɔato din "Avoiding Trigonometry" a programmer Maciej Cegłowski kyerɛwee no gyee mfiridwumayɛfo a wɔwɔ baabiara adwene. Na ɛnyɛ sine ne cosine a ɛyɛ den no ho asɛm, na mmom na ɛfa ɔhaw bi a ɛyɛ anifere kɛse ho: mfiridwuma mu ɛka. Cegłowski kaa ne suahu a ɔde siesiee bɔne bi a ɛnyɛ den wɔ imageboard site a agye din, 4chan no mu kɔɔ akyiri. Ɔdebɔneyɛfo no? Nhyehyɛe a ɛyɛ nwonwa a ɛyɛ ntanta, a wɔayɛ no boro so a wɔde di mfonini a ɛkyinkyini ho dwuma a na ɛde ne ho to nkɔnsɔnkɔnsɔn a ɛyɛ nwonwa a ɛyɛ server-side trigonometry akontaabu so. Na nkrasɛm titiriw no mu dɔ: na wɔn a wɔyɛe no abɔ mmɔden kɛse ayɛ Rube Goldberg afiri bi de akwati ano aduru a ɛnyɛ den na ɛyɛ fɛ a wobetumi anya ntɛm wɔ nnɛyi wɛb brawsa ahorow mu. Saa asɛm yi bɛyɛɛ nhwɛsoɔ a ɛyɛ canonical a ɛkyerɛ sɛdeɛ mfiridwuma a ɛboro soɔ ma ɛyɛ mmerɛw, sɛe nneɛma, na awieeɛ koraa no ɛma nkɔsoɔ brɛ ase kɔ crawl.

Anifere Ho Ka Kɛse

"Avoiding Trigonometry" asɛm no yɛ masterclass wɔ nea efi nyansa a wɔmfa nni dwuma yiye mu ba no mu. Akyinnye biara nni ho sɛ na wɔn a wɔyɛɛ mfitiase nhyehyɛe no ho akokwaw. Wɔde ano aduru a ɛyɛ den dii ɔhaw bi a emu yɛ den ho dwuma. Nanso, wɔn "anifere" mmara no de adesoa a ɛtra hɔ kyɛ bae. Na ɛsɛ sɛ nsakrae biara, mfomso biara a wosiesie, ne ade foforo biara fa saa ntease a ɛyɛ nwonwa yi mu. Bere a mfiase no wɔkoraa so denam ɔkwan a ɛyɛ mmerɛw a wɔanyɛ ho nhwehwɛmu so no, nnɔnhwerew mpempem pii a wɔde hwɛɛ nhyehyɛe a ɛyɛ den no so na wɔyɛɛ ho adwuma no yɛɛ ketewaa. Eyi ne mfiridwuma mu ɛka titiriw —ɛyɛ mfɛntom a wotua wɔ ɔkwan tiawa bi so a na ɛnsɛ sɛ wɔfa da. Wɔ nnɛyi nnwuma fam no, eyi kyerɛ tẽẽ kɔ bere a wɔde kɔ gua so brɛoo ma nneɛma foforo, nkɔso akuw a wɔn abam abu, ne codebase a ɛbɛyɛ asiane na ne bo yɛ den sɛ wɔbɛsesa.

Fapem a Wɔbɛkyekyere a Ɛko Tia Nneɛma a Ɛyɛ Den

Enti, ɛbɛyɛ dɛn na nnwuma atumi akwati wɔn ankasa "Avoiding Trigonometry" no? Mmuae no gyina sɛnea wɔde nneɛma a ɛyɛ mmerɛw ne nea emu da hɔ bedi kan afi mfiase no so. Eyi kyerɛ sɛ wɔbɛkyekyere nhyehyɛe ahorow a ɛhyɛ adansi a ɛho tew na ɛyɛ modular ho nkuran. Ɔkwan a wɔfa so yɛ modular hyɛ nteɛso denam nneɛma a ɛyɛ den a ɛpaapae mu yɛ no nneɛma nketenkete a wotumi di ho dwuma, na wotumi sesa so. Sɛ afã biara wɔ asɛyɛde biako a wɔakyerɛkyerɛ mu yiye a, ɛbɛyɛ mmerɛw sɛ wɔbɛte nhyehyɛe no nyinaa ase, asɔ ahwɛ, na wɔayɛ nsakrae. Eyi ne nyansapɛ a ɛwɔ nnɛyi nhyiam ase a wɔayɛ sɛ ɛbɛma adwumayɛ ayɛ mmerɛw akyi. Sɛ nhwɛso no, Mewayz de modular adwumayɛ OS a ɛboa nnwumakuw ma wɔkwati sɛ wɔbɛkyekye nhyehyɛe ahorow a ɛyɛ ntanta na ɛka bom ma. Ɛdenam module soronko a ɔde ma CRM, adwuma no sohwɛ, ne nkitahodi a ɛka bom a ɛho tew so no, Mewayz hwɛ hu sɛ nsɛm a ɛyɛ den no ahyɛ mu, na ɛnyɛ nea ɛyɛ kɛse.

Efi Mfiridwuma mu Basabasayɛ so kosi Adwumayɛ mu pefeeyɛ so

Asuade a ɛne "Avoiding Trigonometry" no trɛw kɔ akyiri sen server dan no. Ɛyɛ bɛ ma adwuma bi afã horow nyinaa. Sɛ́ ɛyɛ byzantine pene nhyehyɛe, softwea nnwinnade a wɔatwa mu a wɔabɔ no asinasin, anaasɛ dwumadibea nkitahodi kwan a ɛde ne ho to "abusuakuw nimdeɛ" so no, saa nsɛm a ɛyɛ den yi yɛ adwumayɛ a ɛne saa mmara a ɛyɛ tan no yɛ pɛ. Wɔma akasakasa ba, ɛma gyinaesi yɛ brɛoo, na wɔmma ahyehyɛde no ntumi nyɛ adwuma sɛ ade mũ a ɛka bom. Ɛsɛ sɛ botae no yɛ sɛ wɔbɛbɔ nhyehyɛe ahorow—mfiridwuma ne akwan a wɔfa so yɛ adwuma nyinaa—a ɛyɛ mmerɛw na ɛyɛ mmerɛw sɛnea wobetumi. Ɛdenam nhyiam ahorow a wɔpaw a esi nkabom ne nea emu da hɔ so dua, te sɛ Mewayz so no, nnwuma betumi ahwɛ ahu sɛ wɔn adwumayɛ fapem no ma nkɔso tumi sen sɛ ebesiw kwan. Wobetumi de wɔn ahoɔden adi dwuma de akɔ wɔn anim, sen sɛ wɔbɛkyerɛkyerɛ gyinaesi ahorow a ɛyɛ ntanta a atwam no mu bere nyinaa.

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