Although modern scholars have expressed surprise that `` the simple magic square of three '', a mere `` mathematical puzzle '', was able to exert a considerable influence on the minds and imaginations of the cultured Chinese for so many centuries, they could have found most of the answers right within the square itself.

Although he expressed that it would be deeply painful, Pasternak explained that it could not be prevented.

Although expressed in terms of coordinates, the result is invariant under proper rotations of the coordinate axes but the result inverts under reflection.

Although the idea expressed in Cogito ergo sum is widely attributed to Descartes, he was not the first to mention it.

Although artists working with other media have expressed interest in the concept, such as Roy Ascott, " cyberspace " in digital art is mostly used as a synonym for immersive virtual reality and remains more discussed than enacted.

Although the shooter's motives remain unknown, relatives of the shooter had expressed concerns about his mental health.

Although the Casimir effect can be expressed in terms of virtual particles interacting with the objects, it is best described and more easily calculated in terms of the zero-point energy of a quantized field in the intervening space between the objects.

Although expressed in terms of coordinates, the result is invariant under orthogonal transformations, as the physical interpretation suggests.

Although most obituaries were positive, a number of clergymen expressed different sentiments.

Although lightbulb jokes tend to be derogatory in tone, the people targeted by them may take pride in the stereotypes expressed and are often themselves the jokes ' originators.

Although color gamut can be expressed as three pairs of numbers, the XY coordinates within color space of the reddest red, greenest green, and bluest blue, it is usually expressed as a ratio of the total area within color space that a display can show relative to some standard such as saying that a display was " 120 % of NTSC ".

Although originally expressed in Newton's third law, the conservation of linear momentum also holds in special relativity ( with a modified formula ) and, with appropriate definitions, a ( generalized ) linear momentum conservation law holds in electrodynamics, quantum mechanics, quantum field theory, and general relativity.

Although Germany's once-powerful trade unions distanced themselves from the Left in the 2005 election, some union leaders expressed interest in cooperating with the party after the election.

Although he has expressed admiration for many of the values promoted by secular humanism, Singer believes it to be incomplete and promotes a preference utilitarian view he calls " personism " instead.

Although he approved of the doctrine thus expressed, he also ordered that the Nicene Creed, without Filioque, be displayed on silver tablets placed in Saint Peter's Basilica, adding: " Haec Leo posui amore et cautela orthodoxae fidei " ( I, Leo, put these here for love and protection of orthodox faith ).

Although constitutively expressed proteasomes can participate in this process, a specialized complex composed of proteins whose expression is induced by interferon gamma produces peptides of the optimal size and composition for MHC binding.

Although both the exclusivist and the pluralist may agree on the existence of religious or spiritual reality, the pluralist recognizes that this reality is expressed in different cultures and by different people in different ways.

Although stellar parameters can be expressed in SI units or CGS units, it is often most convenient to express mass, luminosity, and radii in solar units, based on the characteristics of the Sun:

Although she expressed a dislike for singing in those bars, Twain believes that this was her own kind of performing arts school on the road.

Although expressed as a problem of software design, the second-system effect is observable throughout all human design effort.

Although the goal is to improve trade, the president of Tajikistan expressed concern that it could also increase drug traffic.

Although they can be written in a completely symbolic form using, for example, propositional calculus, theorems are often expressed in a natural language such as English.

Although the hyperfilament is constructed from " continuous pseudo-one-dimensional diamond crystal ", Clarke later expressed his belief that another type of carbon, Buckminsterfullerene, would play the role of hyperfilament in a real space elevator.

Although strongly urged by moderates in Congress to sign the Civil Rights Bill, Johnson broke decisively with them by vetoing it on March 27.

Although they may not recognize themselves as antiglobalists and are pro-capitalism, some economists who don't share the neoliberal approach of international economic institutions have strongly influenced the movement.

Although Pompey was strongly against it-he wanted to surround and starve Caesar's army instead-he eventually gave in and accepted battle from Caesar on a field near Pharsalus.

Although he was against the actions taken against the veterans and strongly advised MacArthur against taking a public role in it, he later wrote the Army's official incident report, endorsing MacArthur's conduct.

Although he was never a Trotskyist, he was strongly influenced by the Trotskyist and anarchist critiques of the Soviet regime, and by the anarchists ' emphasis on individual freedom.

Although Muslim teaching at this time strongly opposed the printing of Islamic or Arabic texts, non-Muslim printing was not, in principle, forbidden ; indeed attempts were made in the 1570s by anti-Trinitarian Christians to establish a printing press in the Turkish capital to publish radical Protestant works.

Although many people refer to the Inuit language as Eskimo language, this is a broad term that also includes Yupik, and is in addition strongly discouraged in Canada and diminishing in usage elsewhere.

Although some suggested that the diamond should have been presented as a gift to the Queen, it is clear that Dalhousie felt strongly that the stone was a spoil of war, and treated it accordingly.

Although strongly opposed by both the business community and the Conservative Party when introduced in 1999, the minimum wage introduced in the UK is no longer controversial and the Conservatives reversed their opposition in 2000.

Although the economy of Moncton was traumatized twice — by the collapse of the shipbuilding industry in the 1860s and by the closure of the CNR locomotive shops in the 1980s — the city was able to rebound strongly on both occasions.

Although Tchicaya was on the left of the French political spectrum, he never strongly questioned French colonial rule.

Although they are not mentioned by Homer, in a fragment of Hesiod's works they are called brothers of the mountain nymphs and Kuretes, strongly connected with the cult of Dionysus.

Although the book was published years before Patriot Games, there are repeated references to it, which strongly suggests that The Hunt for Red October was in fact written after the Patriot Games manuscript ( or at least the first draft of the novel ) was completed.

Although white dwarfs are known with estimated masses as low as 0. 17 and as high as 1. 33 solar masses, the mass distribution is strongly peaked at 0. 6 solar mass, and the majority lie between 0. 5 to 0. 7 solar mass.

Although not strongly supported in all areas of the country, only UNIP had a nationwide following.

Although most harmony comes about as a result of two or more notes being sounded simultaneously, it is possible to strongly imply harmony with only one melodic line through the use of arpeggios or hocket.

Although the party's conservatives could not stop FDR from winning the nomination, the obvious physical decline in the President's appearance, as well as rumors of secret health problems, led many delegates and party leaders to strongly oppose Henry A. Wallace.

Although public opinion in Paris was strongly against any form of surrender or concession to the Prussians, the Government realised that it could not hold the city for much longer, and that Gambetta's provincial armies would probably never break through to relieve Paris.

Although Greens find much to support in fostering these types of alliances with groups of historically different backgrounds, they also feel strongly about forming diverse communities through encouragement of diversity in social and economic demographics in communities, especially in the United States.

Although this law remains constant, the formula for fusion strongly suggests that it is in fact, not an accurate measure at all.

Although guanxi is associated with the traditional Confucianist doctrine, guanxi ties were strongly developed during the Mao Zedong government ( 1949 – 1976 ), particularly due to the work unit system, which led many workers to construct strong social networks within their units, thus improving their ability to enjoy important resources and privileges.

Although he adamantly refused to be married to Mary, Queen of Scots, Dudley was for a long time relatively sympathetic to her until from the mid-1580s he strongly advocated her execution.

Although ferromagnetic ( and ferrimagnetic ) materials are the only ones attracted to a magnet strongly enough to be commonly considered magnetic, all other substances respond weakly to a magnetic field, by one of several other types of magnetism.

Although Cisco was strongly rooted in the enterprise environment, the company was quick to capture the emerging service provider environment, entering SP market with new, high-capacity product lines such as Cisco 7000 and Cisco 7500.