المرجع الالكتروني للمعلوماتية
المرجع الألكتروني للمعلوماتية

الرياضيات
عدد المواضيع في هذا القسم 9761 موضوعاً
تاريخ الرياضيات
الرياضيات المتقطعة
الجبر
الهندسة
المعادلات التفاضلية و التكاملية
التحليل
علماء الرياضيات

Untitled Document
أبحث عن شيء أخر
{ان أولى الناس بإبراهيم للذين اتبعوه}
2024-10-31
{ما كان إبراهيم يهوديا ولا نصرانيا}
2024-10-31
أكان إبراهيم يهوديا او نصرانيا
2024-10-31
{ قل يا اهل الكتاب تعالوا الى كلمة سواء بيننا وبينكم الا نعبد الا الله}
2024-10-31
المباهلة
2024-10-31
التضاريس في الوطن العربي
2024-10-31


Caroline Lucretia Herschel  
  
100   08:50 صباحاً   date: 7-7-2016
Author : A M Clerke
Book or Source : The Herschels and Modern Astronomy
Page and Part : ...


Read More
Date: 9-7-2016 195
Date: 7-7-2016 29
Date: 7-7-2016 29

Born: 16 March 1750 in Hannover, Hanover (now Germany)
Died: 9 January 1848 in Hannover, Hanover (now Germany)

 

Caroline Herschel was the daughter of Isaac Herschel and Anna Ilse Moritzen. She was sister of William Herschel and the aunt of John Herschel. Caroline's father Isaac was an oboist in the Hanovarian Foot Guards and rose to become the bandmaster. Although a man with no formal education, he tried hard to give his four sons and two daughters a good education. His interests in music, philosophy and astronomy led to lively conversations in their home but Caroline's mother disapproved of learning in general and although she reluctantly accepted that her four sons should have some education, she strongly opposed her daughters doing anything other than the household chores.

Caroline Herschel's four brothers were all brought up to be musicians while Caroline showed an enthusiasm for knowledge which her father tried to satisfy despite all her mother's efforts to ensure that she did nothing but household tasks. Caroline recalled that her father took her [4]:-

... on a clear frosty night into the street, to make me acquainted with several of the beautiful constellations, after we had been gazing at a comet which was then visible.

Caroline could never have thought in her wildest dreams that one day she would make a major contribution to the study of comets.

After the French occupation of Hanover in 1757, Isaac was occupied fighting the French and so was not at home. William escaped to England, where he became a music teacher, and Caroline was left under the control of her mother who sent her to learn to knit and otherwise kept her fully occupied with household chores. In 1760 Isaac returned home in poor health and Caroline essentially lived the life of a servant until he died in 1767. The death of her father seems to have made Caroline realise that she had to take some control of her own life and she took lessons in dressmaking and studied to qualify as a governess. However, fitting in the studies while her mother demanded so much work from her proved a great strain.

In 1766 William became an organist in Bath and, in 1772, Caroline joined him there. She made this move despite strong protests from her mother who was very unhappy at effectively losing a servant. Caroline had always been very close to her brother William and, after arriving in Bath, she trained as a singer receiving lessons from her brother. William taught Caroline more than musical skills. He had studied mathematics and astronomy in his spare time at the end of a long day after many hours teaching music, reading works such as Maclaurin's Fluxions. Now he began to teach Caroline English and mathematics while he himself became more and more involved with astronomy.

Caroline began giving successful singing performances [6]:-

As first treble in the Messiah, Judas Macabaeus, etc., she sang at Bath or Bristol sometimes five nights in the week, but declined an engagement for the Birmingham festival, having resolved to appear only where her brother conducted.

In addition to her singing, Caroline helped William with his musical activities and looked after him while he spent many hours with his new hobby of constructing telescopes. Slowly Caroline turned more and more towards helping William with his astronomical activities while he continued to teach her algebra, geometry and trigonometry. In particular Caroline studied spherical trigonometry which would be important for reducing astronomical observations. However, she was not interested in mathematics for its own sake, finding only those parts which were useful in applications worth studying.

Almost inevitably Caroline's role changed from looking after William to helping him with his scientific activities which soon occupied every available moment. Caroline wrote (see for example [4]):-

Every leisure moment was eagerly snatched at for resuming some work which was in progress, without taking time or changing dress, and many a lace ruffle ... was torn or bespattered by molten pitch. ... I was even obliged to feed him by putting the vitals by bits into his mouth; - this was once the case when at the finishing of a 7 foot mirror he had not left his hands from it for 16 hours ...

Astronomy changed from a hobby for William in 1781 when he achieved fame by discovering the planet now named Uranus. King George III gave William a £200 per year salary which was less than generous but sufficient to allow him to become a full-time astronomer. Giving up their musical activities the Herschels moved to Datchet in August 1782 where they remained until June 1785 when they moved again, this time into Clay Hall, near Windsor. It was certainly not without many regrets that Caroline abandoned music and began to take an active part in astronomy. William gave her a telescope with which she began to make observations, in particular searching for comets making methodical sweeps of the sky.

Caroline found much less time than she expected to make her own observations as she became fully involved helping William with his astronomical projects. By day Caroline would work on the results obtained by William while observing on the previous night. She carried out the lengthy calculations necessary to reduce William's data with remarkable accuracy. In fact only when William was away from home was Caroline able to spend much time with her own program of research. In April 1786 William and Caroline moved to a new home they called Observatory House which was in Slough and there, on 1 August 1786, Caroline discovered her first comet which was described by some as the "first lady's comet". This discovery brought Caroline a certain degree of fame and articles were written about her. In one such article she is described as (see [6]):-

... very little, very gentle, very modest, and very ingenuous...

while another describes her as:-

... a most excellent, kind-hearted creature...

In 1787 King George III gave Caroline a £50 per year salary as assistant to William. In the following year William married Mary Pitt and Caroline's life changed markedly [9]:-

Initially Caroline was deeply affected by the marriage, and moved out to lodgings at Upton. She continued to support her brother's work and in making the daily walk to Observatory House, became a well-known figure. Often, with William resting after a long night of observation, the house was kept as quiet as possible during the day. Eventually the relationship between the two ladies - Mary and Caroline - warmed ...

Caroline kept a diary into which she had recorded her thoughts, in particular she had recorded her great distress at the change in relationship with her brother and she also recorded her bitterness towards his wife. However, as the relationship between the two ladies improved, Caroline regretted her bitter comments against Mary and she destroyed every page of her diary over this time in her life.

In total Caroline discovered eight comets between 1786 and 1797 and she then embarked on a new project of cross-referencing and correcting the star catalogue which had been produced by Flamsteed. In 1798 Caroline submitted to the Royal Society an Index to Flamsteed's Observations of the Fixed Starstogether with a list of 560 stars which had been omitted. This publication marked the temporary end of her own researches which she would not begin again until 25 years later after William's death.

This period of 25 years was not one which lacked interest for Caroline. She became involved with the education of John Herschel, William and Mary Herschel's son who was born in 1792. John Herschel spent long periods with his aunt during the vacations and was greatly influenced by Caroline. She saw him educated at Cambridge, make a name for himself as a mathematician, become elected to the Royal Society, join his father in research in astronomy and be awarded the Copley Medal of the Royal Society for his achievements. Caroline continued to assist William with his observations but her status had greatly improved from the housekeeper she had been in her young days. She was the guest of Maskelyne at the Royal Observatory in 1799 and a guest of members of the Royal Family at various times in 1816, 1817 and 1818.

Caroline returned to Hanover after William's death in 1822. In many ways it was a bad decision, made too quickly, which she soon regretted but she was always one to keep a promise whatever the personal consequences so she would never return to England. All her energies had been directed towards helping her brother in his astronomical work during his lifetime but now she turned to help his son John Herschel. Certainly this help was not given in the same way as a personal assistant, but rather now as independent researcher producing a catalogue of nebulae to assist John in his astronomical work. She completed her catalogue of 2500 nebulae and, in 1828, the Royal Astronomical Society awarded her its gold medal for this work.

Although Caroline regretted spending her last 25 years in Hanover there were many compensations. She was now a celebrity in the world of science and she was visited by many scientists including Gauss. Her nephew John Herschel, visiting Caroline in June 1832 when she was 83 years old, wrote of her (see for example [6]):-

She runs about the town with me, and skips up her two flights of stairs. In the morning, till eleven or twelve, she is dull and weary, but as the day advances she gains life, and is quite 'fresh and funny' at ten p.m., and sings old rhymes, nay, even dances.

Caroline Herschel received many honours for her scientific achievements. Together with Mary Somerville, she was elected to honorary membership of the Royal Society in 1835. They were the first honorary women members. She was also elected a member of the Royal Irish Academy in 1838 and then on her 96thbirthday she received a letter [3]:-

His Majesty the King of Prussia, in recognition of the valuable service rendered to astronomy by you, as the fellow worker of your immortal brother, wishes to convey to you in his name the Large Gold Medal for science.

On her 97th birthday Caroline [6]:-

... entertained the crown prince and princess with great animation for two hours, even singing to them a composition of her brother William.

A minor planet was named Lucretia in 1889 in Caroline Lucretia Herschel's honour, a fitting tribute to one who had contributed so much, yet had so little personal ambition that she disliked praise directed towards her lest it detract from her brother William.


 

  1. M A Hoskin, Biography in Dictionary of Scientific Biography (New York 1970-1990). 
    http://www.encyclopedia.com/doc/1G2-2830901973.html

Books:

  1. A M Clerke, The Herschels and Modern Astronomy (1895).
  2. M C Herschel, Memoir and Correspondence of Caroline Herschel (New York, 1876).
  3. C A Lubbock (ed.), The Herschel Chronicle: The Life-Story of William Herschel and His Sister Caroline Herschel (Cambridge, 1933).
  4. E Pierce, Caroline Herschel : Tale of a Comet (1974).

Articles:

  1. A M Clerke, Caroline Lucretia Herschel, Dictionary of National Biography XXVI (London, 1891), 260-263.
  2. M T A Kempis, Caroline Herschel, Scripta Math. 21 (1955), 246-247.
  3. M B Ogilvie, Caroline Herschel's contributions to astronomy, Ann. of Sci. 32 (1975), 149-161.
  4. F J Ring, John Herschel and his heritage, in D G King-Hele (ed.), John Herschel 1792-1871 : A bicentennial commemoration (London, 1992), 3-16.
  5. J South, An address delivered at the annual general meeting of the Astronomical Society of London on February 8 1829, on presenting the honorary medal to Miss Caroline Herschel, Memoirs of the Royal Astronomical Society 3 (1829), 409-412.

 




الجبر أحد الفروع الرئيسية في الرياضيات، حيث إن التمكن من الرياضيات يعتمد على الفهم السليم للجبر. ويستخدم المهندسون والعلماء الجبر يومياً، وتعول المشاريع التجارية والصناعية على الجبر لحل الكثير من المعضلات التي تتعرض لها. ونظراً لأهمية الجبر في الحياة العصرية فإنه يدرّس في المدارس والجامعات في جميع أنحاء العالم. ويُعجب الكثير من الدارسين للجبر بقدرته وفائدته الكبيرتين، إذ باستخدام الجبر يمكن للمرء أن يحل كثيرًا من المسائل التي يتعذر حلها باستخدام الحساب فقط.وجاء اسمه من كتاب عالم الرياضيات والفلك والرحالة محمد بن موسى الخورازمي.


يعتبر علم المثلثات Trigonometry علماً عربياً ، فرياضيو العرب فضلوا علم المثلثات عن علم الفلك كأنهما علمين متداخلين ، ونظموه تنظيماً فيه لكثير من الدقة ، وقد كان اليونان يستعملون وتر CORDE ضعف القوسي قياس الزوايا ، فاستعاض رياضيو العرب عن الوتر بالجيب SINUS فأنت هذه الاستعاضة إلى تسهيل كثير من الاعمال الرياضية.

تعتبر المعادلات التفاضلية خير وسيلة لوصف معظم المـسائل الهندسـية والرياضـية والعلمية على حد سواء، إذ يتضح ذلك جليا في وصف عمليات انتقال الحرارة، جريان الموائـع، الحركة الموجية، الدوائر الإلكترونية فضلاً عن استخدامها في مسائل الهياكل الإنشائية والوصف الرياضي للتفاعلات الكيميائية.
ففي في الرياضيات, يطلق اسم المعادلات التفاضلية على المعادلات التي تحوي مشتقات و تفاضلات لبعض الدوال الرياضية و تظهر فيها بشكل متغيرات المعادلة . و يكون الهدف من حل هذه المعادلات هو إيجاد هذه الدوال الرياضية التي تحقق مشتقات هذه المعادلات.