Re: [tmoz:411712] elips

cevrel cember elips nasıl olursa olsun FF' ortalayan doğru (x=a,Y=b )
içteğet cember ise FF'  asal eksen kabul eden elips

ben bunları buldum zaman olursa yazayım öyle cok ispata erek yok gibi...

24 Mart 2011 17:55 tarihinde erdal karaburun (Öğretmen) <ekaraburun@gmail.com> yazdı:

benim gördüğüm bir şeyde şu M noktasında çizilen teğet o köşedeki dış açıortay oluyor.ama F den çizilen iç açıortayla  veya diğer F' köşesindeki dış açıortayın kesim noktasını ifade edebilirsek sanırım iş çözülür..ilgiilendiğiniz için çok teşekkür ederim...

24 Mart 2011 17:54 tarihinde erdal karaburun (Öğretmen) <ekaraburun@gmail.com> yazdı:

benim gördüğüm bir şeyde şu M noktasında çizilen teğet o köşedeki dış açıortay oluyor.ama F den çizilen teğetle veya diğer F' köşesindeki dış açıortayın kesim noktasını ifade edebilirsek sanırım iş çözülür..ilgiilendiğiniz için çok teşekkür ederim...

24 Mart 2011 17:48 tarihinde Muharrem Şahin <muharrem49@gmail.com> yazdı:

Erdal Hocam;
İçteğet çemberin  merkezinin FF' nü büyük
eksen sayan bir elips olacağını söylemiştim.
Bir bakışta söylenebilecek bu sonucun ispatlanması gerekir.
Aralıklarla da olsa hep sentetik bir ispat üzerinde düşündüm.
Ama bu çok zor gibi.
Analitik yoldan ispatladım.
Elipsin denkleminde M'nin koordinatlarının yerine,
bu koordinatların çemberin merkezinin koordinatları türünden
değeri konulunca, asal akseni FF' olan elips denklemi çıkıyor.
Bu koordinatları yazmak zoruna giderse yazarım.
Selamlar

23 Mart 2011 22:52 tarihinde erdal karaburun (Öğretmen)

<ekaraburun@gmail.com> yazdı:
> 1971 baskısı bir lise kitabı.yazar yok..alıştırma
> soruları..:)..ilgilenirseniz undan sonra diğer konularla ilgili
> alıştırmalarıda paylaşmak isterim..
>
> 23 Mart 2011 22:45 tarihinde murat yalcin(öğretmen) <gmuratyalcin@gmail.com>
> yazdı:
>>
>> genel halini söylersem (ben bu soruyu cok sevdem kaynağı neymıs )
>>  cevrel cember elips nasıl olursa olsun FF' ortalayan doğru (x=a,Y=b )
>> içteğet cember ise FF'  asal eksen kabul eden elips
>>
>> 23 Mart 2011 22:35 tarihinde murat yalcin(öğretmen)
>> <gmuratyalcin@gmail.com> yazdı:
>>>
>>> merkezcil elips dersek asal eksenin  xekseni dunursek
>>> cevrel cember   geometrik y ekseni
>>> içteğet cember   geometrik yeri ASAl Ekseni F,F olan elips
>>> asal eksen y ise tam terleri...
>>>
>>> 23 Mart 2011 22:30 tarihinde Muharrem Şahin <muharrem49@gmail.com> yazdı:
>>>>
>>>> İçteğet çemberin merkezinin geometrik yerinin odakları birleştiren
>>>> doğru parçasını asal eksen sayan bir elips olacağı görülüyor.
>>>> Tam ispatları düşüneceğim.
>>>>
>>>>
>>>> 23 Mart 2011 22:24 tarihinde murat yalcin(öğretmen)
>>>> <gmuratyalcin@gmail.com> yazdı:
>>>> > merkezlarinin geometrik yeri dersek:
>>>> >
>>>> > 23 Mart 2011 22:23 tarihinde murat yalcin(öğretmen)
>>>> > <gmuratyalcin@gmail.com>
>>>> > yazdı:
>>>> >>
>>>> >> hocam nasıl soru bu:)???
>>>> >>
>>>> >> 23 Mart 2011 22:13 tarihinde erdal karaburun (Öğretmen)
>>>> >> <ekaraburun@gmail.com> yazdı:
>>>> >>>
>>>> >>> iyi..:) herkes burdayken bi sorum daha var.değişen bir M noktası
>>>> >>> odakları
>>>> >>> F ve F' olan bir elips çizmektedir.MFF' üçgeninin iç teğet ve dış
>>>> >>> teğet
>>>> >>> çemberlerinin geometrik yeri?
>>>> >>>
>>>> >>> 23 Mart 2011 22:10 tarihinde Muharrem Şahin <muharrem49@gmail.com>
>>>> >>> yazdı:
>>>> >>>>
>>>> >>>> Murat Hocam;
>>>> >>>> Açık konuşayım.
>>>> >>>> Çok yan yana geldik;bir selamı bile esirgedin.
>>>> >>>> Ama belki bana öyle gelmiştir.
>>>> >>>> Güzelliklerin sürmesini diliyorum.
>>>> >>>>
>>>> >>>> 23 Mart 2011 22:06 tarihinde murat yalcin(öğretmen)
>>>> >>>> <gmuratyalcin@gmail.com> yazdı:
>>>> >>>> > niye ayda yıldamı guzel konusuyom:)  bizde guzel bi söz vardır
>>>> >>>> > Hakkın(doğrunun) hakkı alidir hiç bir seye feda edilmez:) biz
>>>> >>>> > yanlıs
>>>> >>>> > dudunmusuz
>>>> >>>> >
>>>> >>>> >
>>>> >>>> > 23 Mart 2011 22:03 tarihinde Muharrem Şahin
>>>> >>>> > <muharrem49@gmail.com>
>>>> >>>> > yazdı:
>>>> >>>> >>
>>>> >>>> >> Murat Hocam,
>>>> >>>> >> Senin ağzından güzel şeyler duymak gerçekten çok güzel.
>>>> >>>> >>
>>>> >>>> >> 23 Mart 2011 22:01 tarihinde murat yalcin(öğretmen)
>>>> >>>> >> <gmuratyalcin@gmail.com> yazdı:
>>>> >>>> >> > evet muharrem abi cok haklısınız...
>>>> >>>> >> >
>>>> >>>> >> > 23 Mart 2011 21:58 tarihinde Muharrem Şahin
>>>> >>>> >> > <muharrem49@gmail.com>
>>>> >>>> >> > yazdı:
>>>> >>>> >> >>
>>>> >>>> >> >> Murat Hocam;
>>>> >>>> >> >> Dediğiniz gibi, asal eksen x veya y ekseni de olmak zorunda
>>>> >>>> >> >> değil.
>>>> >>>> >> >> Asal çemberin merkezinden geçen herhangi bir doğru olabilir.
>>>> >>>> >> >>
>>>> >>>> >> >> 23 Mart 2011 21:55 tarihinde murat yalcin(öğretmen)
>>>> >>>> >> >> <gmuratyalcin@gmail.com> yazdı:
>>>> >>>> >> >> > evet fatih hocam ya x asal eksen yada y asal eksen
>>>> >>>> >> >> >
>>>> >>>> >> >> > 23 Mart 2011 21:53 tarihinde fatih çelik
>>>> >>>> >> >> > <fatihprof@gmail.com>
>>>> >>>> >> >> > yazdı:
>>>> >>>> >> >> >>
>>>> >>>> >> >> >> iki tane olmuyor mu sayın hocam?
>>>> >>>> >> >> >>
>>>> >>>> >> >> >> 23 Mart 2011 21:51 tarihinde murat yalcin(öğretmen)
>>>> >>>> >> >> >> <gmuratyalcin@gmail.com> yazdı:
>>>> >>>> >> >> >>>
>>>> >>>> >> >> >>> söyle dusunelim asal cemberi xkare+ykare=25 olan x+y=4
>>>> >>>> >> >> >>> doğrusuna
>>>> >>>> >> >> >>> teğet
>>>> >>>> >> >> >>> olan elipsin denklemi
>>>> >>>> >> >> >>>
>>>> >>>> >> >> >>> a=5  teğetlik kosulundanda b bulunur... ben mi yanlıs
>>>> >>>> >> >> >>> dusuunyorum...
>>>> >>>> >> >> >>> ...
>>>> >>>> >> >> >>>
>>>> >>>> >> >> >>> 23 Mart 2011 21:48 tarihinde erdal karaburun (Öğretmen)
>>>> >>>> >> >> >>> <ekaraburun@gmail.com> yazdı:
>>>> >>>> >> >> >>>>
>>>> >>>> >> >> >>>> sanırım çizilebilir Muharrem Hocam çemberin merkezi ve
>>>> >>>> >> >> >>>> geçtiği bir
>>>> >>>> >> >> >>>> nokta
>>>> >>>> >> >> >>>> belirlenebilirse çizilebilir gibi..yinede murat hocam bi
>>>> >>>> >> >> >>>> açıklama
>>>> >>>> >> >> >>>> yapar
>>>> >>>> >> >> >>>> inşallah...
>>>> >>>> >> >> >>>>
>>>> >>>> >> >> >>>> 23 Mart 2011 21:44 tarihinde Muharrem Şahin
>>>> >>>> >> >> >>>> <muharrem49@gmail.com>
>>>> >>>> >> >> >>>> yazdı:
>>>> >>>> >> >> >>>>>
>>>> >>>> >> >> >>>>> Ben Murat Hocam'ın kafasının çok iyi çalıştığını
>>>> >>>> >> >> >>>>> biliyorum.
>>>> >>>> >> >> >>>>> O zaman benim çözümümün yanlış olması gerekir.
>>>> >>>> >> >> >>>>> Bana bir teğet ve asal çemberle elipsin denklemi
>>>> >>>> >> >> >>>>> yazılamaz
>>>> >>>> >> >> >>>>> gibi
>>>> >>>> >> >> >>>>> geliyor.
>>>> >>>> >> >> >>>>> Murat Hocam yazarsa hatamızı görmüş oluruz.
>>>> >>>> >> >> >>>>> Sevgiler, saygılar.
>>>> >>>> >> >> >>>>>
>>>> >>>> >> >> >>>>> 23 Mart 2011 21:37 tarihinde murat yalcin(öğretmen)
>>>> >>>> >> >> >>>>> <gmuratyalcin@gmail.com> yazdı:
>>>> >>>> >> >> >>>>> > ben bilmem ama asal cembrti ve bir teğeti verilen
>>>> >>>> >> >> >>>>> > elipsin
>>>> >>>> >> >> >>>>> > denklemini
>>>> >>>> >> >> >>>>> > bulurum
>>>> >>>> >> >> >>>>> > sanırm kafam durmamıssa...
>>>> >>>> >> >> >>>>> >
>>>> >>>> >> >> >>>>> > 23 Mart 2011 21:31 tarihinde erdal karaburun
>>>> >>>> >> >> >>>>> > (Öğretmen)
>>>> >>>> >> >> >>>>> > <ekaraburun@gmail.com> yazdı:
>>>> >>>> >> >> >>>>> >>
>>>> >>>> >> >> >>>>> >> Murat hocam genel ir hal sorulmuş sanırım..Muharrem
>>>> >>>> >> >> >>>>> >> hocamın
>>>> >>>> >> >> >>>>> >> çözümü
>>>> >>>> >> >> >>>>> >> sanırım
>>>> >>>> >> >> >>>>> >> elipsi sabitliyor...
>>>> >>>> >> >> >>>>> >>
>>>> >>>> >> >> >>>>> >> 23 Mart 2011 21:26 tarihinde murat yalcin(öğretmen)
>>>> >>>> >> >> >>>>> >> <gmuratyalcin@gmail.com> yazdı:
>>>> >>>> >> >> >>>>> >>>
>>>> >>>> >> >> >>>>> >>> yoo ben sadace neden 2 teğet diye sordum:)
>>>> >>>> >> >> >>>>> >>>
>>>> >>>> >> >> >>>>> >>> 23 Mart 2011 21:25 tarihinde murat yalcin(öğretmen)
>>>> >>>> >> >> >>>>> >>> <gmuratyalcin@gmail.com> yazdı:
>>>> >>>> >> >> >>>>> >>>>
>>>> >>>> >> >> >>>>> >>>> muglaklık tan kastım su asal cemberi  ....... olan
>>>> >>>> >> >> >>>>> >>>> teğetlerinden
>>>> >>>> >> >> >>>>> >>>> biri
>>>> >>>> >> >> >>>>> >>>> yada (ikisi) sulan elipsin denklemi diye sorsa
>>>> >>>> >> >> >>>>> >>>> sanırm
>>>> >>>> >> >> >>>>> >>>> daha
>>>> >>>> >> >> >>>>> >>>> anlasılar olur...
>>>> >>>> >> >> >>>>> >>>>
>>>> >>>> >> >> >>>>> >>>> 23 Mart 2011 21:23 tarihinde Muharrem Şahin
>>>> >>>> >> >> >>>>> >>>> <muharrem49@gmail.com>
>>>> >>>> >> >> >>>>> >>>> yazdı:
>>>> >>>> >> >> >>>>> >>>>>
>>>> >>>> >> >> >>>>> >>>>> Erdal Hocam;
>>>> >>>> >> >> >>>>> >>>>> Verilen teğetlerin asal çemberi kestiği
>>>> >>>> >> >> >>>>> >>>>> noktalardan
>>>> >>>> >> >> >>>>> >>>>> bu teğetlere dikmeler çizerseniz, bunla ikişer
>>>> >>>> >> >> >>>>> >>>>> ikişer
>>>> >>>> >> >> >>>>> >>>>> elipsin odaklarında kesişirler. Böylece odaklar
>>>> >>>> >> >> >>>>> >>>>> bulunmuş
>>>> >>>> >> >> >>>>> >>>>>  olur. Gerisi tamamlanır sanıyorum.
>>>> >>>> >> >> >>>>> >>>>>
>>>> >>>> >> >> >>>>> >>>>> 23 Mart 2011 20:31 tarihinde erdal karaburun
>>>> >>>> >> >> >>>>> >>>>> (Öğretmen)
>>>> >>>> >> >> >>>>> >>>>> <ekaraburun@gmail.com> yazdı:
>>>> >>>> >> >> >>>>> >>>>> > asal çemberi ve iki teğeti verilen elipsi
>>>> >>>> >> >> >>>>> >>>>> > çiziniz...şimdiden
>>>> >>>> >> >> >>>>> >>>>> > teşekkürler..
>>>> >>>> >> >> >>>>> >>>>> >
>>>> >>>> >> >> >>>>> >>>>> > --
>>>> >>>> >> >> >>>>> >>>>> > Milli varlığımızın temelini;milli şuurda ve
>>>> >>>> >> >> >>>>> >>>>> > milli
>>>> >>>> >> >> >>>>> >>>>> > birlikte
>>>> >>>> >> >> >>>>> >>>>> > görmekteyiz.
>>>> >>>> >> >> >>>>> >>>>> > Mustafa Kemal ATATÜRK
>>>> >>>> >> >> >>>>> >>>>> >
>>>> >>>> >> >> >>>>> >>>>> >
>>>> >>>> >> >> >>>>> >>>>> >
>>>> >>>> >> >> >>>>> >>>>> > --
>>>> >>>> >> >> >>>>> >>>>> >
>>>> >>>> >> >> >>>>> >>>>> >
>>>> >>>> >> >> >>>>> >>>>> >
>>>> >>>> >> >> >>>>> >>>>> >
>>>> >>>> >> >> >>>>> >>>>> >
>>>> >>>> >> >> >>>>> >>>>> > http://www.facebook.com/pages/Matematik-Geometri/150709609688?ref=mf
>>>> >>>> >> >> >>>>> >>>>> >
>>>> >>>> >> >> >>>>> >>>>>
>>>> >>>> >> >> >>>>> >>>>> --
>>>> >>>> >> >> >>>>> >>>>>
>>>> >>>> >> >> >>>>> >>>>>
>>>> >>>> >> >> >>>>> >>>>>
>>>> >>>> >> >> >>>>> >>>>>
>>>> >>>> >> >> >>>>> >>>>>
>>>> >>>> >> >> >>>>> >>>>> http://www.facebook.com/pages/Matematik-Geometri/150709609688?ref=mf
>>>> >>>> >> >> >>>>> >>>>
>>>> >>>> >> >> >>>>> >>>>
>>>> >>>> >> >> >>>>> >>>>
>>>> >>>> >> >> >>>>> >>>> --
>>>> >>>> >> >> >>>>> >>>>
>>>> >>>> >> >> >>>>> >>>>  Derdin mi var? " Lâ tahzen innallâhe meanâ " (
>>>> >>>> >> >> >>>>> >>>> Üzülme
>>>> >>>> >> >> >>>>> >>>> Allah
>>>> >>>> >> >> >>>>> >>>> bizimledir
>>>> >>>> >> >> >>>>> >>>> )
>>>> >>>> >> >> >>>>> >>>
>>>> >>>> >> >> >>>>> >>>
>>>> >>>> >> >> >>>>> >>>
>>>> >>>> >> >> >>>>> >>> --
>>>> >>>> >> >> >>>>> >>>
>>>> >>>> >> >> >>>>> >>>  Derdin mi var? " Lâ tahzen innallâhe meanâ " (
>>>> >>>> >> >> >>>>> >>> Üzülme
>>>> >>>> >> >> >>>>> >>> Allah
>>>> >>>> >> >> >>>>> >>> bizimledir )
>>>> >>>> >> >> >>>>> >>>
>>>> >>>> >> >> >>>>> >>> --
>>>> >>>> >> >> >>>>> >>>
>>>> >>>> >> >> >>>>> >>>
>>>> >>>> >> >> >>>>> >>>
>>>> >>>> >> >> >>>>> >>>
>>>> >>>> >> >> >>>>> >>>
>>>> >>>> >> >> >>>>> >>> http://www.facebook.com/pages/Matematik-Geometri/150709609688?ref=mf
>>>> >>>> >> >> >>>>> >>
>>>> >>>> >> >> >>>>> >>
>>>> >>>> >> >> >>>>> >>
>>>> >>>> >> >> >>>>> >> --
>>>> >>>> >> >> >>>>> >> Milli varlığımızın temelini;milli şuurda ve milli
>>>> >>>> >> >> >>>>> >> birlikte
>>>> >>>> >> >> >>>>> >> görmekteyiz.
>>>> >>>> >> >> >>>>> >> Mustafa Kemal ATATÜRK
>>>> >>>> >> >> >>>>> >>
>>>> >>>> >> >> >>>>> >>
>>>> >>>> >> >> >>>>> >>
>>>> >>>> >> >> >>>>> >> --
>>>> >>>> >> >> >>>>> >>
>>>> >>>> >> >> >>>>> >>
>>>> >>>> >> >> >>>>> >>
>>>> >>>> >> >> >>>>> >>
>>>> >>>> >> >> >>>>> >> http://www.facebook.com/pages/Matematik-Geometri/150709609688?ref=mf
>>>> >>>> >> >> >>>>> >
>>>> >>>> >> >> >>>>> >
>>>> >>>> >> >> >>>>> >
>>>> >>>> >> >> >>>>> > --
>>>> >>>> >> >> >>>>> >
>>>> >>>> >> >> >>>>> >  Derdin mi var? " Lâ tahzen innallâhe meanâ " (
>>>> >>>> >> >> >>>>> > Üzülme
>>>> >>>> >> >> >>>>> > Allah
>>>> >>>> >> >> >>>>> > bizimledir )
>>>> >>>> >> >> >>>>> >
>>>> >>>> >> >> >>>>> > --
>>>> >>>> >> >> >>>>> >
>>>> >>>> >> >> >>>>> >
>>>> >>>> >> >> >>>>> >
>>>> >>>> >> >> >>>>> >
>>>> >>>> >> >> >>>>> > http://www.facebook.com/pages/Matematik-Geometri/150709609688?ref=mf
>>>> >>>> >> >> >>>>> >
>>>> >>>> >> >> >>>>>
>>>> >>>> >> >> >>>>> --
>>>> >>>> >> >> >>>>>
>>>> >>>> >> >> >>>>>
>>>> >>>> >> >> >>>>>
>>>> >>>> >> >> >>>>> http://www.facebook.com/pages/Matematik-Geometri/150709609688?ref=mf
>>>> >>>> >> >> >>>>
>>>> >>>> >> >> >>>>
>>>> >>>> >> >> >>>>
>>>> >>>> >> >> >>>> --
>>>> >>>> >> >> >>>> Milli varlığımızın temelini;milli şuurda ve milli
>>>> >>>> >> >> >>>> birlikte
>>>> >>>> >> >> >>>> görmekteyiz.
>>>> >>>> >> >> >>>> Mustafa Kemal ATATÜRK
>>>> >>>> >> >> >>>>
>>>> >>>> >> >> >>>>
>>>> >>>> >> >> >>>>
>>>> >>>> >> >> >>>> --
>>>> >>>> >> >> >>>>
>>>> >>>> >> >> >>>>
>>>> >>>> >> >> >>>>
>>>> >>>> >> >> >>>> http://www.facebook.com/pages/Matematik-Geometri/150709609688?ref=mf
>>>> >>>> >> >> >>>
>>>> >>>> >> >> >>>
>>>> >>>> >> >> >>>
>>>> >>>> >> >> >>> --
>>>> >>>> >> >> >>>
>>>> >>>> >> >> >>>  Derdin mi var? " Lâ tahzen innallâhe meanâ " ( Üzülme
>>>> >>>> >> >> >>> Allah
>>>> >>>> >> >> >>> bizimledir )
>>>> >>>> >> >> >>>
>>>> >>>> >> >> >>> --
>>>> >>>> >> >> >>>
>>>> >>>> >> >> >>>
>>>> >>>> >> >> >>>
>>>> >>>> >> >> >>> http://www.facebook.com/pages/Matematik-Geometri/150709609688?ref=mf
>>>> >>>> >> >> >>
>>>> >>>> >> >> >> --
>>>> >>>> >> >> >>
>>>> >>>> >> >> >>
>>>> >>>> >> >> >> http://www.facebook.com/pages/Matematik-Geometri/150709609688?ref=mf
>>>> >>>> >> >> >
>>>> >>>> >> >> >
>>>> >>>> >> >> >
>>>> >>>> >> >> > --
>>>> >>>> >> >> >
>>>> >>>> >> >> >  Derdin mi var? " Lâ tahzen innallâhe meanâ " ( Üzülme
>>>> >>>> >> >> > Allah
>>>> >>>> >> >> > bizimledir
>>>> >>>> >> >> > )
>>>> >>>> >> >> >
>>>> >>>> >> >> > --
>>>> >>>> >> >> >
>>>> >>>> >> >> >
>>>> >>>> >> >> > http://www.facebook.com/pages/Matematik-Geometri/150709609688?ref=mf
>>>> >>>> >> >> >
>>>> >>>> >> >>
>>>> >>>> >> >> --
>>>> >>>> >> >>
>>>> >>>> >> >>
>>>> >>>> >> >> http://www.facebook.com/pages/Matematik-Geometri/150709609688?ref=mf
>>>> >>>> >> >
>>>> >>>> >> >
>>>> >>>> >> >
>>>> >>>> >> > --
>>>> >>>> >> >
>>>> >>>> >> >  Derdin mi var? " Lâ tahzen innallâhe meanâ " ( Üzülme Allah
>>>> >>>> >> > bizimledir
>>>> >>>> >> > )
>>>> >>>> >> >
>>>> >>>> >> > --
>>>> >>>> >> >
>>>> >>>> >> >
>>>> >>>> >> > http://www.facebook.com/pages/Matematik-Geometri/150709609688?ref=mf
>>>> >>>> >> >
>>>> >>>> >>
>>>> >>>> >> --
>>>> >>>> >>
>>>> >>>> >> http://www.facebook.com/pages/Matematik-Geometri/150709609688?ref=mf
>>>> >>>> >
>>>> >>>> >
>>>> >>>> >
>>>> >>>> > --
>>>> >>>> >
>>>> >>>> >  Derdin mi var? " Lâ tahzen innallâhe meanâ " ( Üzülme Allah
>>>> >>>> > bizimledir )
>>>> >>>> >
>>>> >>>> > --
>>>> >>>> >
>>>> >>>> > http://www.facebook.com/pages/Matematik-Geometri/150709609688?ref=mf
>>>> >>>> >
>>>> >>>>
>>>> >>>> --
>>>> >>>>
>>>> >>>> http://www.facebook.com/pages/Matematik-Geometri/150709609688?ref=mf
>>>> >>>
>>>> >>>
>>>> >>>
>>>> >>> --
>>>> >>> Milli varlığımızın temelini;milli şuurda ve milli birlikte
>>>> >>> görmekteyiz.
>>>> >>> Mustafa Kemal ATATÜRK
>>>> >>>
>>>> >>>
>>>> >>>
>>>> >>> --
>>>> >>> http://www.facebook.com/pages/Matematik-Geometri/150709609688?ref=mf
>>>> >>
>>>> >>
>>>> >>
>>>> >> --
>>>> >>
>>>> >>  Derdin mi var? " Lâ tahzen innallâhe meanâ " ( Üzülme Allah
>>>> >> bizimledir )
>>>> >
>>>> >
>>>> >
>>>> > --
>>>> >
>>>> >  Derdin mi var? " Lâ tahzen innallâhe meanâ " ( Üzülme Allah
>>>> > bizimledir )
>>>> >
>>>> > --
>>>> > http://www.facebook.com/pages/Matematik-Geometri/150709609688?ref=mf
>>>> >
>>>>
>>>> --
>>>> http://www.facebook.com/pages/Matematik-Geometri/150709609688?ref=mf
>>>
>>>
>>>
>>> --
>>>
>>>  Derdin mi var? " Lâ tahzen innallâhe meanâ " ( Üzülme Allah bizimledir )
>>
>>
>>
>> --
>>
>>  Derdin mi var? " Lâ tahzen innallâhe meanâ " ( Üzülme Allah bizimledir )
>>
>> --
>> http://www.facebook.com/pages/Matematik-Geometri/150709609688?ref=mf
>
>
>
> --
> Milli varlığımızın temelini;milli şuurda ve milli birlikte görmekteyiz.
> Mustafa Kemal ATATÜRK
>
>
>
> --
> http://www.facebook.com/pages/Matematik-Geometri/150709609688?ref=mf
>

--
http://www.facebook.com/pages/Matematik-Geometri/150709609688?ref=mf

--

Milli varlığımızın temelini;milli şuurda ve milli birlikte görmekteyiz.
Mustafa Kemal ATATÜRK

--
Milli varlığımızın temelini;milli şuurda ve milli birlikte görmekteyiz.
Mustafa Kemal ATATÜRK

--
http://www.facebook.com/pages/Matematik-Geometri/150709609688?ref=mf

--

 Derdin mi var? " Lâ tahzen innallâhe meanâ " ( Üzülme Allah bizimledir )

--
http://www.facebook.com/pages/Matematik-Geometri/150709609688?ref=mf