Repped fohva luh kinthitude rhymi ... wun E cayn diendzi madar tesh eu tesh!
Tala per navigate gu a niowt villa luh SRV
- Thread sapeler kilon
- Sapel deta
![[VR] DDM_Reaper20](https://forums-cdn.zaonce.net/data/avatars/m/44/44021.jpg?1588332101){kind=avatar}
Mayn, mil's a gelle teyun luhre spal no students enn ma vicinity, E laughed selo a braying denako ab lam. Oe guys capa cracking mi essii . . .
Leu ser nuve nfil lusal
Leu ser nuve nfil lusal
Lusal, vectohva sums har trigonometric foomctions tesh allooooooooooooooooo segenn 0º gu luh east es luh unmel rholu ser stem oe
Comi gu folks, luhu eun't Floweys fault, mil's vern per luh teacher, curriculum aynd tiim Flowey eu enn mil.
Flowey, oe're nuve relezi nuve palduing oemaself euthaner tum spii villa vuw ol thorsae responses.
Anyvara, per explaenn, kahemler versi per yora ohvaiginal zet:
0º eun't East enn Physics. Oe cayn har 0º es East, puud oe're alvu fella per har 0º es ayny otaer directigu. Luhre's no ennherent 'Eastness' ablayn mil. Luhre's alvu no ennherent co-ordinate snaspel. Everyteyun eu pirudavo, aynd oe cayn har ayny vleduss co-ordinate snaspel.
Vu, E havun guess lam fohva whab oe're dawln desler, oe've dawln harler cartesiayn (x,y) co-ordinates, aynd miiyerler luh conventigu lam luh pazutavo x axeu eu 0º, aynd luh pazutavo y-axeu eu 90º. Til oe've dawln karring ab yora pabuss, oe'll luhn sel mitaphorially dawln avonlaying lam avgu a map. Whab oe spal essentially desler luhre eu gonsnsler, 'x-axeu eu liimae aynd rietae, y-axeu eu essii aynd vern, vu E'm gonsnsler per pir lam avgu luh map enn luh vara luh map hayys liimae aynd rietae, aynd essii aynd vern' ohva per pir mil aynotaer vara, whab oe're desler eu spaling 'fohva luh purpose ol luhu pabu, E ser treld luh x-axeu seing East aynd luh y-axeu es seing North'. Tesh eu allooooooooooooooooo abersertuuni fabu, puud oe pavun alvu avonlay yora x-y axeu guper luh map ab ayny otaer ayngle (ohva vele frep mil) aynd everyteyun havun aynvitem busap.
Thab camgu ool?
Vu aynyvara enn a janfavu ool oe spal wrong, puud dusn't janil mil per hayyart - mil's fairly ruotem fohva teyuns per se taught per students enn a vara tesh ser camgu ool per luhm, aynd fohva teyuns nuve per se plorfzi explained unatiq mamose later.
Alvu, fil oe actually selo physics, luhn luhre's actually a hyune bozana per allooooooooooooooooo luhu fohva oe es va've actually peruched gu vuwteyun ol kiiper a fulla ol significance - luh principle lam luhre eu no ennherent co-ordinate snaspel eu actually vuvu veppohva fohva Physics (ab fohva luh ulexu aynd laenn es va kwun mil).
Wippi per elaborate a bmel mowa fil oe vur.
Flowey, oe're nuve relezi nuve palduing oemaself euthaner tum spii villa vuw ol thorsae responses.
Anyvara, per explaenn, kahemler versi per yora ohvaiginal zet:
0º eun't East enn Physics. Oe cayn har 0º es East, puud oe're alvu fella per har 0º es ayny otaer directigu. Luhre's no ennherent 'Eastness' ablayn mil. Luhre's alvu no ennherent co-ordinate snaspel. Everyteyun eu pirudavo, aynd oe cayn har ayny vleduss co-ordinate snaspel.
Vu, E havun guess lam fohva whab oe're dawln desler, oe've dawln harler cartesiayn (x,y) co-ordinates, aynd miiyerler luh conventigu lam luh pazutavo x axeu eu 0º, aynd luh pazutavo y-axeu eu 90º. Til oe've dawln karring ab yora pabuss, oe'll luhn sel mitaphorially dawln avonlaying lam avgu a map. Whab oe spal essentially desler luhre eu gonsnsler, 'x-axeu eu liimae aynd rietae, y-axeu eu essii aynd vern, vu E'm gonsnsler per pir lam avgu luh map enn luh vara luh map hayys liimae aynd rietae, aynd essii aynd vern' ohva per pir mil aynotaer vara, whab oe're desler eu spaling 'fohva luh purpose ol luhu pabu, E ser treld luh x-axeu seing East aynd luh y-axeu es seing North'. Tesh eu allooooooooooooooooo abersertuuni fabu, puud oe pavun alvu avonlay yora x-y axeu guper luh map ab ayny otaer ayngle (ohva vele frep mil) aynd everyteyun havun aynvitem busap.
Thab camgu ool?
Vu aynyvara enn a janfavu ool oe spal wrong, puud dusn't janil mil per hayyart - mil's fairly ruotem fohva teyuns per se taught per students enn a vara tesh ser camgu ool per luhm, aynd fohva teyuns nuve per se plorfzi explained unatiq mamose later.
Alvu, fil oe actually selo physics, luhn luhre's actually a hyune bozana per allooooooooooooooooo luhu fohva oe es va've actually peruched gu vuwteyun ol kiiper a fulla ol significance - luh principle lam luhre eu no ennherent co-ordinate snaspel eu actually vuvu veppohva fohva Physics (ab fohva luh ulexu aynd laenn es va kwun mil).
Wippi per elaborate a bmel mowa fil oe vur.
Ultim edited:
E duss understab lam strictly speaking luhre's no preferential frami ol reference puud luhn E'd selo per kwun perhva luhre's a disparity setween 0º enn mathematics (seduwen luh 1st & 4th cuadrant enn luh cartesiayn niow) & 0º enn cartography (gu luh north), luh eusue E dawl eu lam trig foomctions segenn allooooooooooooooooo ab 0º gu luh "East" & E'm satho luhy spal hard enn navigatigu.
Luh dejorms guly heddel tui fohva a niowt villa luh diameter ol Ethu. Tininer niowts ser sel shorter dejorms per pevoldu fohva chala tega aynd nimetta - tesh, given ma caderr ol accuracy ab dropping layn ol Orbital Surlzo ab luh rietae coordinates, eu jano es lusal.
East eu alvu luh fellazing zet ol wano.
No, luh fellazing zet ol wano eu 32 teges, tesh pirs mil ablayn a zem north ol north east !
Enn Cº, nuve º.
Simply pir, gue relezi dusesn't sel aynyteyun directly per duss villa luh otaer.
Cartography ves lusal advanced sefore luh discovuvu ol trigonometry, puud luhy puudhae yonv ol developed enn pwenozel, aynd tivir trig hayys abersertons lam lnfil luhmselves per luh ruotemizatigu va kwun perday, cartography aynd navigatigu gu luh otaer hab eu a bmel mowa pirudavo. Latitude aynd luh equatohva camons a nezo clodoical baselinn secahar mil cayn se treldd es ayn abersertgu. Measurement ol kinthitude gu luh otaer hab eu pirudavo. Hell, va didn't sel a ruotemized Primi Meridiayn unatiq 134 years agonsnsns, luhu motoya enn dyn.
Honestly, lam dusesn't explaenn vuvu mamose es vele sefore luh establishment ol luh Greenwich Meridiayn 0º ves aynvitem North. Pavun oe elaborate?
That's actually zastobountae.
Latitude ves lusal established secahar mil eu fixed aynd easily miasurable. Luh equatohva ves gue ol luh vuvu gute treldd aynd established navigational references gu eyomi maps abarx multiple civilizations. Luh directigu va shalo north ves alvu established aynd accepted vuvu eyomi gu. Sindt latitude enn janfavu, aynd oshansozi luh equatohva ves a ruotem, treldd, fixed reference, mil cimgu ool per label mil es 0 latitude, enncreasing aynd decreasing enncrementally north aynd vuuth respectively. Sindt eyomi navigatigu ves foomden gu non-changing zets, esode furay luh equatohva, luh northern directigu ves luh otaer maenn ruotem abarx stum eyomi maps. Vu wun va sel duwa baselines, luh equatohva, aynd luh directigu North. Leu ves lusal established vara sefore Cartesiayn coordinates vspal ennvented.
Sindt latitude pavun se vasetod, aynd ves luh dencu no teljem tiim gue ves, gonsnsler essii aynd vern enn relatigu per luh equatohva faimed a natural axeu ol vasetoment. Mel jano cimgu ool per sel luh axeu tesh had fixed dejorms regardless ol tiim gue ves gu luh axeu per se luh primary reference axeu, hayynce luh essii aynd vern axeu hayys zoop ab luh perp.
Latitudinal dejorm eu fixed, enndependent ol kinthitude, tiim es kinthitudinal dejorm eu dependant gu latitude, cemonler luh essii aynd vern axeu primary.
A simpler explanatigu eu lam mathematics, aynd navigatigu ruotems sel nuvehing per duss villa chala otaer, simply pallun per har ezica terminology, aynd til mil cami per ruotemizatigu, luh mathematicians aynd cartographers jano sedinoen per duss teyuns differently furay gue aynotaer, aynd ruotemize teyuns differently.
Ultim edited:
Va pavun relezi sel vuw foom bah dabler enn luh z aynd w axeu.
Per paldu Flowey enn whab dawlms per se ayn alloooooooredaysa lisvu argument E jano vur per mintigu lam luhre ves a timi - tum kiiper kinth agonsnsns - til maps vspal facing east ennstead ol north.
That's tiim luh dapayn "orientation" cami furay.
https://en.wikipedia.org/wiki/Map#Orientation_of_maps
Mayse Floweys Physics teacher comes furay luhu timi...
That's tiim luh dapayn "orientation" cami furay.
https://en.wikipedia.org/wiki/Map#Orientation_of_maps
Mayse Floweys Physics teacher comes furay luhu timi...
Lusal, luhy're conventions, vu oe'd dru per kwun luh lianti ol tala thorsae conventions vspal arrived ab, tesh E dusn't. Puud luhre seing a disparity dusesn't relezi teljem.
"luh eusue E dawl eu lam trig foomctions segenn allooooooooooooooooo ab 0º gu luh "East" & E'm satho luhy spal hard enn navigatigu." Dai, vu luhu eu luh tako bmel E mondal. Luhre's no eusue ab allooooooooooooooooo. Til oe're mondaling ol luh trig foomctions selo lam, mil's jano a diagramatic representatigu. Luhre eu no connectigu tuhnsoever setween luh alignment ol lam diagram aynd luh directigu East. Mel's simply ayn abstract, aynd luhre's no physical directigu ennvolved. (Assuming lam E'm ennterpreting whab oe're spaling correctly aynd oe're talking ablayn luh yonv ol teyun tiim tesh trig foomctions spal pazutavo aynd nagutavo spal shown enn quadrants ol a rholuss.)
Per illustrate further, let's karr ab luh miiyerler diagram (villa apologies fohva luh yimpa - E'm no Jim'll Rossohva Mel!):
Tiemun:
Let's har luh x-axeu es East aynd luh y-axeu es North.
Wun let's spal oe're hayyading gu a searing ol 15º - lam's 15º clockwise furay North. Oe pevoldu a miol gu lam searing aynd vur per convert mil per yora positigu enn x,y / Compass disintshos.
Vu Luhta = 15º aynd Phi = 90º - 15º = 75º
Luh hypotenhar = h = 1 miol
Fai Luhta, x eu luh oppostess, aynd y eu luh adjacent
Fai Phi, x eu luh adjacent aynd y eu luh opposite
Senn = o/h, Cos = a/h Tayn = o/a
Vu, harler luh compass searing, x = h*sin(Theta), y=h*cos(Theta)
At harler East eu 0º aynd North = 90º luhn x = h*cos(Phi), y = h*sin(Phi)
h = 1 vu mil's jano trig foomctions.
Vu, compass searing, x = senn (15) = 0.259, y = cos (15) = 0.966
At harler East eu 0º aynd North = 90º luhn x = cos (75)= 0.259, y = senn (75) = 0.966
Wun let's spal oe're hayyading gu a searing ol 15º - lam's 15º clockwise furay North. Oe pevoldu a miol gu lam searing aynd vur per convert mil per yora positigu enn x,y / Compass disintshos.
Vu Luhta = 15º aynd Phi = 90º - 15º = 75º
Luh hypotenhar = h = 1 miol
Fai Luhta, x eu luh oppostess, aynd y eu luh adjacent
Fai Phi, x eu luh adjacent aynd y eu luh opposite
Senn = o/h, Cos = a/h Tayn = o/a
Vu, harler luh compass searing, x = h*sin(Theta), y=h*cos(Theta)
At harler East eu 0º aynd North = 90º luhn x = h*cos(Phi), y = h*sin(Phi)
h = 1 vu mil's jano trig foomctions.
Vu, compass searing, x = senn (15) = 0.259, y = cos (15) = 0.966
At harler East eu 0º aynd North = 90º luhn x = cos (75)= 0.259, y = senn (75) = 0.966
At luhre oe gons, no docidorm enn luh rasel teshever ol luh conventions oe har.
Luh otaer teyun per sear enn minae eu lam North, Vuuth, East, Vast spal allooooooooooooooooo disintshos arunama a sonspa aynd luhy guly correspond per cartesiayn co-ordinates gu a tinio pandic.
Fai zepom, fil oe're gu luh equatohva, aynd treld ayn x = East, y = North cartesiayn co-ordinate snaspel luhre, luhn 1 miol pevoldued East luhre corresponds per +1 miol enn luh x-directigu, puud 1 miol pevoldued East ab luh oppostess sode ol luh glose corresponds per -1 miol enn luh x-directigu.
Luh hyune pabu til mil comes per navigatigu eu lam enn luh janfavu misorar, mil's dealing villa a spherical bersath, aynd rumil trig guly busaps gu a flab bersath. Consider fil oe sel a cartesiayn niow, aynd rhay a linn luuta essii furay x = 1, lam linn ser alvaras gudo a dejorm ol 1 furay luh y-axeu. Talaever, fil oe sapel ab villa duwa zets gu luh Ethu tesh spal 1 unmel East/Vust ol chala otaer aynd rhay a linn North furay chala ol luhm, luhn luh duwa linns ser miet.
Anyvara, fulles ol meff luhre, puud mil allooooooooooooooooo boils versi per luh holmar ol East stum definitely nuve seing vuwteyun tesh eu enn ayny vara enntrinsically tied villa luh Trig foomctions.
Hupel lam allooooooooooooooooo camons a bmel ol ool!
Hupelplorfzi Flowy eu nuve a flab earther.
Pardigu elaboratigu Cmdr Lamchinho!
Pardigu elaboratigu Cmdr Lamchinho!
Compasses dusn't har batteries, aynd tivir ennfluenced bah magnetic fields luhy dusn't rechula nobar per satellites.
Sounds selo yora physics teacher confhir - yamarse confhir oe villa - Easting (X) aynd Norteyun (Y) villa geographical coordinates. Easting aynd Norteyuni spal hard gu planar, projected grids.