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Charles Solomon: Mathematics
Hamlyn all-colour paperbacks
Paul Hamlyn, The Hamlyn Publishing Group Ltd - London, 1969
Explore Aug 1, 2012 #170
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“Happiness is when what you think, what you say, and what you do are in harmony.” by Mahatma Gandhi
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“Always aim at complete harmony of thought and word and deed. Always aim at purifying your thoughts and everything will be well.” by Mahatma Gandhi
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“In the end we shall have had enough of cynicism, skepticism and humbug, and we shall want to live more musically.” by Vincent van Gogh
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“Mathematics expresses values that reflect the cosmos, including orderliness, balance, harmony, logic, and abstract beauty.” by Deepak Chopra
Messing about on the river at Cambridge's Mathematical Bridge. I felt I was lucky to be on Silver Street bridge as this punt came into sight with the chaps wearing straw boaters.
Mathematical and Geometrical Problems, The Iconographic Encyclopedia of Science, Literature and Art c. 1851 Copyright free.
Sierpinski gasket. The 10th of 25 mathematic Lego mini mosaics (20 inches square). When completed the entire montage will stretch over 42 feet. (THIS IS A 3-D AND DIFFICULT TO PHOTOGRAPH FROM ABOVE)
This picture came out a bit too dark.. I should have better light when working.
I think the paper is from a Barbie office table set?
Hyperbolic Crochet
Hyperbolic Double Spiral
(Unfurled View)
Yellow Wool
increased one stitch in every five
started with 16 stitches
19 rows
The University of Greenwich is a public university located in London and Kent, United Kingdom. Previous names include Woolwich Polytechnic and Thames Polytechnic.
The university's main campus is at the Old Royal Naval College, which along with its Avery Hill campus, is located in the Royal Borough of Greenwich. Greenwich also has a satellite campus in Medway, Kent, as part of a shared campus. The university's range of subjects includes architecture, business, computing, mathematics, education, engineering, humanities, maritime studies, natural sciences, pharmacy and social sciences. Greenwich's alumni include two Nobel laureates: Abiy Ahmed and Charles K. Kao. It received a Silver rating in the UK government's Teaching Excellence Framework.
The university dates back to 1891, when Woolwich Polytechnic, the second-oldest polytechnic in the United Kingdom, opened in Woolwich. It was founded by Frank Didden, supported by and following the principles of Quintin Hogg, and opened to students in October 1891. Like Hogg's pioneering venture in London's Regent Street, it initially combined education with social and religious functions.
In 1894 it focused on an educational role, concentrating on higher technical education appropriate to its location close to Woolwich Dockyard and the Royal Arsenal; William Anderson, director-general of the Ordnance Factories, was a trustee and later a member of the board of governors. Its premises were also used for day schools – the first Woolwich Polytechnic School was established in 1897.
In 1970, Woolwich Polytechnic merged with part of Hammersmith College of Art and Building to form Thames Polytechnic. In the following years, Dartford College (1976), Avery Hill College of Education (1985), Garnett College (1987) and parts of Goldsmiths College and the City of London College (1988) were incorporated.[9]
In 1992, Thames Polytechnic was granted university status by the Major government (together with various other polytechnics) and renamed the University of Greenwich in 1993. On 1 January 1993, the Thames College of Health Care Studies, itself a merger of three local nursing and midwifery training schools, officially merged with the newly designated University of Greenwich, becoming a full faculty of the university.
Formerly a UK government research agency, the Natural Resources Institute (NRI) was incorporated into the university in 1996.
In 2001, the university gave up its historic main campus in the Bathway Quarter in Woolwich, relocating to its current main campus in Greenwich.
Greenwich Campus is located mainly in the Old Royal Naval College, into which it moved in the 1990s when the premises were sold by the Royal Navy.
The campus is home to the Business School and the Faculty of Liberal Arts and Sciences. The campus also includes university's Greenwich Maritime Institute, a specialist maritime management, policy and history teaching and research institute. The Old Royal Naval College also hosts "The Painted Hall", which was painted in the 18th century by Sir James Thornhill, which covers over 40,000 square feet of surface in 200 painting of kings, queens and mythological creatures.
The campus has a large library at Stockwell Street which houses an extensive collection of books and journals, language labs and a 300-PC computing facility. Other facilities include specialist computer laboratories including one at Dreadnought centre, a TV studio and editing suites. The Stephen Lawrence Gallery at the Stockwell Street building, showcases the work of contemporary artists and is linked to the School of Design.
The Avery Hill Campus comprises two sites, Mansion and Southwood. Both are situated in the 86-acre Avery Hill Park in the Royal Borough of Greenwich, south-east London.
The campus is home to the Faculty of Education & Health. Facilities include computer laboratories, a library and a TV studio, as well as a sports and teaching centre with a sports hall and 220-seat lecture theatre. Southwood site also has clinical skills laboratories. These replicate NHS wards, enabling trainee health professionals to gain hands-on experience. The village complex provides student accommodation, a general shop and a launderette. The Dome, in the centre of the complex, houses a food outlet and gym. Rugby, football, indoor pitches, netball and tennis courts, and a dance studio are on Avery Hill campus.
The facility, which was built by Wimpey Construction under a PFI contract, was completed in 1996.
The Winter Garden, the centrepiece of the Mansion site, has fallen into neglect and is on Historic England's 'At Risk' Register. A campaign to restore the Winter Garden is putting pressure on the university and Greenwich Council to ensure its future.
The Medway Campus is located on a former Royal Navy shorebase (called HMS Pembroke) opened in 1903 at Chatham Maritime, Kent.
The Faculty of Engineering and Science is based here, as is the Natural Resources Institute, a centre for research, consultancy and education in natural and human resources. It is also the home of Medway School of Pharmacy, a joint school operated by the Universities of Greenwich and Kent. The Faculty of Education & Health offers a number of its programmes at Medway. Facilities include laboratories, workshops, a computer-aided design studio and a training dispensary.
The Drill Hall Library is a learning resource centre with a library, computers, study areas and teaching rooms. Social facilities include a sports hall, bar, gym and outdoor tennis courts. The university is a member of Universities at Medway, a partnership of educational establishments at Chatham Maritime that is developing the area as a major higher education centre in the Medway region.
Greenwich Campus is near 74-hectare Greenwich Park, home to the Royal Observatory, Greenwich. The Stockwell Street Building opened in 2014 and is now home to the campus library, film and TV studios, and state-of-the-art editing suites. In 2015, it was shortlisted for the Stirling Prize for excellence in architecture.
The Dreadnought Building is a central hub for the Greenwich Campus, with further teaching and social spaces.
The Student Village at Avery Hill Campus provides accommodation for around 1,000 students. On-site facilities include a café, canteen, shop, launderette, bicycle parking, and a gym.
Medway Campus has 350 rooms across five halls of residence dedicated to student accommodation.
Greenwich Students' Union is the university's students' union. In October 2019, the GSU Student Assembly voted to ask the university to declare a climate emergency and for the university and union sustainability strategies to consult with students in creating them. This call to action aimed to speed up the university's efforts at becoming carbon neutral.
At the Medway campus in Kent there is a partnership between the University of Greenwich Students' Union, Canterbury Christ Church and University of Kent Union on the Medway campus. Greenwich Students' Union has been leading the partnership since July 2021 and manages The Hub space, previously The Student Hub when it was looked after by GK Unions – the Greenwich & Kent Students' Unions Together (once the Universities at Medway Students Association, UMSA).
Greenwich Students' Union delivers at Avery Hill, Greenwich and Medway campus.
Greenwich research seeks to influence and enhance health, education, science, engineering, computing and social policy, and attracts international agencies, government departments and global corporations (for example, Pfizer, GlaxoSmithKline, BAE Systems, Airbus, GE Aviation and Merck Consumer Health) from over 50 countries. Significant areas of research and consultancy include landscape architecture, employment relations, fire safety, natural resources, tourism and hospitality, social network analysis, education, training, educational leadership and public services.
Examples of research
The university's Natural Resources Institute has developed an artificial cow that attracts and kills the tsetse fly. This was recognised by a Universities UK survey in 2009 as one of the ten most important discoveries to be made in a UK university over the past 60 years.
The Fire Safety Engineering Group, part of the School of Computing & Mathematical Sciences, is a world leader in computational fire engineering, including expertise in aircraft, building, ship and rail evacuation and fire modelling. It has developed airEXODUS, a leading evacuation model in the aviation industry.
A University of Greenwich research team helped restore the Cutty Sark after it was badly damaged by fire.
Researchers working on 19 sustainable development and agriculture projects in India helped the university to win the 2010 Times Higher Education Award for Outstanding International Strategy.
Two University of Greenwich scientists have developed a technology which converts contaminated land and industrial waste into harmless pebbles, capturing large amounts of carbon dioxide at the same time.
The Greenwich Maritime Institute makes internationally recognised contributions to research in maritime history and economics, such as its exploration of the governance of the River Thames since the 1960s and the effects this has had on the economic development of adjacent communities.
The university has had many famous movie productions that were filmed on campus, one example of a movie is the classic 2013 Marvel movie Thor: Dark World
Rankings
Rankings
National rankings
Complete (2024)110
Guardian (2024)116
Times / Sunday Times (2024)105
Global rankings
ARWU (2023)601–700
QS (2024)671–680
THE (2024)501–600
The university was ranked 94 out of 121 UK institutions according to The Guardian University Guide 2022 league table. For 2023, the University of Greenwich was ranked 60 according to Times Higher education (THE). Moreover, University of Greenwich ranked first in London for Events, Tourism and Hospitality by the Guardian’s 2023 university rankings. Subjects taught at Greenwich have seen rises in the Guardian university league tables for 2022: Chemistry was at 10, up 10 places since 2021. Forensic Science (9), Criminology (10), Mechanical Engineering (12), and Education (48) also moved up significantly.
In Center for World University Rankings World University Rankings 2020–21 – University of Greenwich was ranked 76 in the UK. In 2022, University of Greenwich was ranked in the 750-800 range globally by QS World University Rankings.
In the Times Higher Education (THE) Impact Rankings 2020, Greenwich performed well in several categories:
Responsible Consumption and Production (24th)
Life on Land (66th)
Reduced Inequalities (68th)
Climate Action (75th)
Partnership for the Goals (77th)
Awards
In 2012, the university was rated as the greenest in the UK by People & Planet Green League Table. In 2019, it was ranked 14 in UK, and third in London. The University has gained many national awards, including four Queen's Anniversary Prizes, nine Times Higher Education Awards and two Guardian University Awards.
In 2019, the university's Natural Resources Institute was awarded a Queen's Anniversary Prize for its research in pest management and control to combat human and animal diseases in the UK and internationally; in 2015 it won a prize for work on the cassava crop in Africa.
In 2023, the university has been classified as Gold in Teaching Excellence Framework (TEF) of Higher Education.
Cafeteria workers' dispute
In 2019, the university's main cafeteria was operated by BaxterStorey, which paid its workers £9.25 per hour without contractual sick pay. After a chef had collapsed on his way home from a shift during a typical 80-hour week, all workers joined UVW union. After four strike days in October 2019, and protests disrupting the annual graduation ceremony and a board meeting, Greenwich University announced in early January 2020 that all outsourced cafe workers, cleaners and security guards would receive the London living wage of £10.55, in addition to the same sick pay and annual leave as university staff.
Partnership with Charlton Athletic
In 2018, the University of Greenwich started a partnership with Charlton Athletic F.C.
Notable alumni
Abiy Ahmed is Prime Minister of Ethiopia and a Nobel Peace prize winner
Sir Charles Kao was one of the distinguished alumni at UOG
Demitu Hambisa Bonsa
Prominent alumni of the university and its predecessor organisations include Nobel Laureate Charles Kao, who was awarded the Nobel Prize in Physics in 2009 for his work on transmission of light in fibre optics, and Abiy Ahmed, who won the 2019 Nobel Peace Prize. In June 2021, representatives from multiple countries called for the award of the Nobel Peace Prize to Abiy to be re-considered because of the war crimes committed in Tigray. Two British government ministers, Richard Marsh and Gareth Thomas, are also graduates. A more extensive list is given below.
Abiy Ahmed, Prime Minister of Ethiopia and Nobel Peace prize winner
Jamie 'JME' Adenuga, MC
Bola Agbaje, playwright
Helen Bailey, writer
Natasha Bedingfield, pop singer (did not graduate)
John Behr, theologian
Malorie Blackman, children's author
Demitu Hambisa Bonsa, Ethiopian government minister
John Boyega, actor, best known for Star Wars: The Force Awakens
Sheila Bromberg, musician
Liam Brown, author
Campbell Christie, chairman of Falkirk F.C.
Terry Christian, radio and television presenter
Mark Daly, Irish senator
Siobhan Dowd, writer (A Swift Pure Cry)
Sarah Eberle, garden designer
Jenni Fagan, author
Leo Fortune-West, professional footballer
Sarah Gillespie, singer-songwriter
Pippa Guard, actress
Andrey Guryev (born 1982), Russian entrepreneur
Gareth Hale, comedian
Patrick Harrington, politician in the National Front (1979–1989) and currently Third Way (UK) think tank; general secretary of Solidarity – The Union for British Workers
Rachael Heyhoe-Flint, cricketer
Roy Hodgson, England and Premier League football manager
Dermot Hudson, left-wing political activist
Brian Jacks, 1972 Summer Olympics bronze medallist in Judo
Mark Jackson, musician (VNV Nation)
Charles K. Kao, Nobel Prize winning scientist
Graham Kendrick, Christian worship leader
Sammy Lee, IVF specialist
Pablo Daniel Magee, writer, journalist and playwright
Richard Marsh, Baron Marsh, politician
Rui Moreira, Portuguese politician and businessman; mayor of Porto
Chinenye Ochuba, former Most Beautiful Girl in Nigeria
Sarah Ockwell-Smith, childcare author
Joy Onumajuru, model and philanthropist
Norman Pace, comedian
Ann Packer, 1964 Summer Olympics gold medallist
Lara Pulver, Olivier Award-nominated dancer and actress
Richard Pybus, cricket coach
George Rose, businessman
Dave Rowntree, musician (Blur)
Etienne Schneider, Deputy Prime Minister of Luxembourg
Peter Skinner, MEP
Aramazd Stepanian, playwright
William G. Stewart, TV presenter (Fifteen to One)
Nina Stibbe, author
Adelle Stripe, author
Gareth Thomas, politician
Ewen Whitaker, lunar astronomer (alumnus of Woolwich Polytechnic)
Joel Willans, author and copywriter of works in Finland.
A few photos from a trip in 2015 inside the Andrew Wiles Building in Oxford, named after the man who solved Fermat's Last Theorem
From Mathematical Models, 2nd Edn, by H. M. Cundy and A.P. Rollett, Oxford University Press, 1951.
The notations are by my father, as he worked out measurements to build models.
Post is here: blog.ounodesign.com/2009/04/29/stellated-polyhedra-mathem...
A very cool idea in mathematics that is worth looking up is that of space filling curves or Peano curves first described by Giuseppe Peano.
The specific curve depicted here is due to David Hilbert, and is so called a Hilbert curve.
This turned out kinda wierd, kinda neat, hopefully not gruesome.
The Mandelbrot Set, possibly the most famous example of a fractal, was, like the word "fractal", introduced by the mathematician Benoit Mandelbrot, an employee of IBM back when corporations thought mathematical research might be useful. (It was! Today Google & Microsoft sponsor a fair amount of research. Not mine, alas: I'm happily useless.) According to James Gleick's book "Chaos", Mandelbrot's interest in fractals began while he investigated noise on phone lines; he noticed self-similarity in the noise's geometry, and this led him off on a tangent that these days gives us beautiful ties. Back in the 80s and 90s, many a SunStation was brought to its knees under the weight of Mandelbrot and Julia sets being computed by computer geeks who wanted to show off the pretty colors to their girfriends. (I never did this, but a friend of mine loathed Mandelbrot sets for this reason. Also because he thought them otherwise useless.)
Image created using particles obeying certain "gravitational" laws. Mostly variations on "accelerate toward/away from some particle unless some condition is met, in which case move toward/away from some other particle".
Made with processing (processing.org).
Here's that transitional Ollie I was talking about earlier, from one bench to the other. Too bad it was such a grey day, but thank god it didn't rain.
by Internet Archive Book Images
Most people agree that fractions are a bugbear in mathematics. Wherever they rear their ugly heads, they wreak havoc on both novice and expert alike. So how can we show that the non-terminating repeating decimal 0.999… is exactly equal to the number 1? ...
Teaching math processes to Grade 2 students at East Bay Waldorf School.
Blogged at: thewaldorfway.blogspot.com/2010/04/grade-two-math.html
Ahmad ibn ‘Ali ibn Yusuf al-Buni (Arabic: أحمد البوني) (died 1225) was a well known Sufi and writer on the esoteric value of letters and topics relating to mathematics, sihr (sorcery) and spirituality, but very little is known about him. Al-Buni lived in Egypt and learned from many eminent Sufi masters of his time.
He wrote one of the most famous books of his era, the Shams al-Ma'arif al-Kubra (Sun of the Great Knowledge, Arabic شمس المعارف الكبرى) which is one of the most widely read medieval treatises on talismans, magic squares and occult practices. This work rivals the Picatrix in importance. This book was later banned by orthodox Muslims as heretical, but continues to be read and studied.
Instead of sihr (Sorcery), this kind of magic was called Ilm al-Hikmah (Knowledge of the Wisedom), Ilm al-simiyah (Study of the Divine Names) and Ruhaniyat (Spirituality). Most of the so-called mujarrabât ("time-tested methods") books on sorcery in the Muslim world are simplified excerpts from the Shams al-ma`ârif. The book remains the seminal work on Theurgy and esoteric arts to this day.
In c. 1200, Ahmad al-Buni showed how to construct magic squares using a simple bordering technique, but he may not have discovered the method himself. Al-Buni wrote about Latin squares and constructed, for example, 4 x 4 Latin squares using letters from one of the 99 names of Allah. His works on traditional healing remains a point of reference among Yoruba Muslim healers in Nigeria and other areas of the Muslim world.
Ahmad al-Buni also left a list of other titles that he wrote. Unfortunately, very few of them have survived.
Al-Buni states in his work Manba’ Usul al-Hikmah (Source of the Essentials of Wisdom) that he acquired his knowledge of the esoteric properities of the letters from his personal teacher Abu Abdillah Shams al-Din al-Asfahâni. He in turn received it from Jalal al-Din Abdullah al-Bistami, who in turn received it from Shaykh al-Sarajani, who received it from Qasim al-Sarajani, who received it from Abdullah al-Babani, who received it from Asîl al-Din al-Shirazi, who received it from Abu al-Najîb al-Sahruwardi, who received it from, Mohammad ibn Mohammad Al-Ghazali al-Tusi, who received it from Ahmad al-Aswad, who received it from Hamad al-Dînuri, who received it from the master al-Junayd al-Baghdadi, who received it from Sari al-Din al-Saqati, who received it from Ma’ruf al-Karkhi, who received it from Dawûd al-Jili, who received it from Habîb al-A’ajami, who received it from Imam Hasan al-Basri.
Al-Buni states in the same work that he acquired his knowledge of magical squares from Sirâj al-Dîn al-Hanafi, who acquired it from Shihab al-Dîn al-Muqaddasi, who acquired it from Shams al-Dîn al-Farisi, who acquired it from Shihab al-Dîn al-Hamadani, who acquired it from Qutb al-Dîn al-Diyâ’i, who acquired it from Muhyiddîn Ibn Arabi, who acquired it from Abu al-'Abbas Ahmad ibn al-Turîzi, who acquired it from Abu Abdillah al-Qurashi, who acquired it from Abu Madîn al-Andalusi.
He also states that he acquired additional knowledge about the esoteric art of letters and the magical squares from Mohammad 'Izz al-Dîn ibn Jam’a, who acquired it from Mohammad al-Sirani, who acquired it from Shihab al-Dîn al-Hamadani, who acquired it from Qutb al-Dîn al-Dhiya’i, who acquired it from Muhyiddîn Ibn Arabi.
Al-Buni also states that he acquired his occult knowledge from Abu al-'Abbas Ahmad ibn Maymûn al-Qastalâni, who acquired it from Abu Abdillah Mohammed al-Qurashi, who acquired it from Abu Madîn Shu'ayb ibn Hasan al-Ansari al-Andalusi, who received it from Abu Ayyub ibn Abi Sa'id al-Sanhaji al-Armuzi, who received it from Abi Muhammad ibn Nur, who received it from Abu al-Fadhl Abdullah ibn Bashr, who received it from Abu Bashr al-Hasan al-Jujari, who received it from al-Saqati, who received it from Dawûd al-Tâ’i, who received it from Habîb al-A'jami, who received it from Abu Bakr Muhammad ibn Sîrîn, who received it from Malik ibn Anas.
Al-Buni also made regular mention in his work of Plato, Aristotle, Hermes, Alexander the Great, and obscure Chaldean magicians. In one of his works, he recounted a story of his discovery of a cache of manuscripts buried under the pyramids, that included a work of Hermetic thinkers.
His work is said to have influenced the Hurufis and the New Lettrist International.