GeoGebra, ilimin lissafi a motsi

geogebra software ne na geometry mai kuzari, ma'ana, yana bamu damar yin gine-ginen lissafi kuma mu basu rai (karanta "ku rayar dasu") don kawai mu kai ga kyakkyawar fahimtar ilimin lissafi amma kuma don aiwatarwa hadaddun aiki da kwaikwayo ko dai daga wasu yankuna na Lissafi ko wasu fannoni kamar su Turanci ko Tattalin arziki.


Wasu lokuta sukan tambaye ni dalilin yanke shawarar yin karatun Lissafi kuma hoton ya zama mai maimaituwa. Ina kokarin bayyana menene a gareni dalilai ne masu sauƙi da gamsarwa: ta yaya ba zan ƙaunaci Lissafi ba idan a ciki kuna iya yaba kyakkyawa mai kyau-mafi kyau amma mai kyau-, idan ma'abocin gaskiya ne kuma malamin tsabtarwa da tsari, idan yana koyarwa tunani, sadarwa kuma ku zama masu kirkira (…)?: Amma bayan 'yan mintoci kaɗan wanda a ciki na gwada ta hanyar da ta fi ta ɗan adam don sa abokin magana na ya fahimci aƙalla ɗaya daga cikin muradi na, sai ya yi sauri ya canza batun. Idan dokar matsakaita gaskiya ce, babu wasu ƙalilan daga cikinmu waɗanda suke da sha'awar Lissafi har suka mai da shi babban aikinmu. Kodayake gaskiya ne cewa yana da matukar wahala ga "dalibi na zamani" ya sami wannan dandano na musamman a gare shi ko kuma a zahiri ya fahimci wani bangare na babban jigogin da yake rufewa, duk ba a rasa ba. Wani komputa mai ban sha'awa na ilimin lissafi yazo daga Faransa: GeoGebra don "sanya kirji" ga irin wannan ƙalubalen.

GeoGebra shiri ne mai cike da tsari, wanda ke nufin cewa da shi zamu iya samar da gine-gine daga maki, bangarori, layuka, da dai sauransu. da kuma rayar da su don sake kirkirar tsari daban-daban na lissafi don haka koya mafi kyau ko koyar da dabarun da ake so. Amma ba a nan kawai ya tsaya ba; yana kuma iya amfani da lissafi da algebra a cikin yanayi mai motsi.

Ana iya shigar da abubuwa ko dai tare da danna maɓallin nunawa a cikin zane ko kuma yin nazari a cikin na'ura mai kwakwalwa mai sauƙi amma mai aiki sosai. Adadin kayan aikin da GeoGebra yake aiki da su don sarrafa abubuwa yana da ban sha'awa har ya zuwa kusan cewa babu wani abu da ya tsere wa masu haɓaka shi (wanda Markus Hohenwarter ya jagoranta) har ta kai ga cewa ba ƙari ba ne cewa za a iya yin wani abu da za a iya tsammani a 2D a GeoGebra .

Amma GeoGebra ya wuce gaba: ana iya ƙirƙirar rayarwa ta atomatik da gabatarwa, ana iya fitar da gine-ginenta zuwa nau'ikan amfani daban-daban kamar PNG, mai rai GIF, EPS, PDF, PsTricks (ee, yana fitarwa zuwa lambar LaTeX !!!), Da sauransu. ; har ma da abubuwan waje (kamar su hotuna) ana iya shigo da su cikin aikin lissafi.

Hanyoyin sa suna da sauki da dadi. A ciki zamu sami hangen nesa, yanayin algebraic kuma, idan ana so, ra'ayin maƙunsar bayanai.

Wannan GeoGebra yana wasa tare da wasu ra'ayoyi iri iri na lissafin Euclidean (bisectors na bangarorin da mai zagaye):

Anan tare da wasu abubuwa na lissafi (aikin jiji, abin ƙyamarsa, haɗe yake daga sifili zuwa pi da kusanci ta hanyar jerin Taylor):

Anan yin kwaikwayon kimiyyar lissafi (wani madubi mai rikitarwa):

Capabilitiesarfin GeoGebra na iya gamsar da kowane mai sauraro na kowane matakin. Idan mai amfani ya buƙaci haka, zai iya wakilta - har ma idan yana shirye ya sami babban matakin kula da shirin - fractals da abubuwa da kwaikwayo a 3D (koda kuwa an tsara shi don 2D !!!).

En http://www.geogebratube.org/?lang=es Akwai babbar kundin bayanai na ayyukan da yawancin masu sha'awar shirin suka yi, waɗanda aka rarraba ta rukuni-rukuni kuma wasu daga cikinsu suna da ban sha'awa sosai.

Nau'in GeoGebra na yanzu shine 4.0.32.0 kuma ta hanyar mashahuri buƙata, don sigar 5 na shirin akwai tuni akwai ƙarin, mai sauƙi amma mai ƙarfi yanayi don yin duk abin da za'a iya tsammani a cikin 3D (beta ya riga ya kasance kuma yayi alƙawari da yawa).

Don samun GeoGebra, kawai kalli mai sarrafa kunshin datar ku kuma da alama shirin yana da dannawa ɗaya ne kawai. Idan wannan ba batunku bane, akan shafin yanar gizon aikin http://www.geogebra.org/cms/es zaka iya samun damar kunshin da umarnin don ƙara wuraren ajiye su.

Ba na so in ƙara ɗaukar lokaci, abokina; don haka ina fatan in kara muku kwarin gwiwa ku kalli Lissafi daga yanzu da idanu daban albarkacin GeoGebra. Idan kun riga kun so wannan kyakkyawar fagen ilimin, ina taya ku murna; Amma idan wannan ba batunku bane, ku ba GeoGebra dama domin ta wannan ne zaku fahimci yadda wannan horon ya zama abin birgewa ga mai girma Galileo wanda ya bayyana shi a matsayin "harshen Duniya".

Na gode Carlos Andrés Pérez Montaña don gudummawar!
Sha'awan ba da gudummawa?

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  1.   Luis Roberto Perez Rios m

    Very kyau

  2.   Farashin 7017 m

    Kyakkyawan software don ilimin lissafi da fahimta.

  3.   gon m

    Wannan yayi kyau! suna ba da gudummawa don sanya abubuwa su zama abin nishaɗi wanda da yawa suna da ban dariya lol: D ... Kada ku yi fushi da abin mamaki! 😉