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英文を読んで、その数学的内容を述べなくてわいけないのですが、その訳にあまり自信がないので、チェックしていただきたいのでが・・・。 INVERSECSION Convention We use the term inversion to mean either reflection in a line or inversion in a circle. The following gives a geometric method for constructing inverse points with respect to a given circle. Let a be a point outside a circle S with centre c and rather r, let a∨p and a∨q be the two tangents from a to S, and let a’ be the point of intersection of c∨a and p∨q. Then a and a’ are inverse with respect to S. For, in the triangles △cpa’ and △cap, the angles at c are equal and the two angles ∠ca’p ∠cpa are equal, since they are both right angles; hence all the angles in the two triangles are equal. Thus the triangles are similar; hence, in particular, we must have that ｜→ca’｜/｜→cp｜=｜→cp｜/｜→ca｜, so that ｜→ca｜・｜→ca’｜=｜→cp｜^2=r^2. Thus a and a’ are inverse with respect to S, as claimed. We end this subsection by showing that an invention in circle is a difficult type of transformation from those that arise in Euclidean and affine geometry. First, an inversion in a circle is not an affine transformation since it does not map lines to lines. For example, let S be the unit circle and L be the line with equation Re(z)=2. All the points on L lie outside the unit circle and so invention in S must map all the points of L to points that lie inside the unit circle. In particular, the image of L cannot be a line. Thus, since the image of a line under any affine transformation is itself a line, it follows that inversion cannot be an affine transformation. An inversion in a circle is not a Euclidean transformation either, for like affine transformation, Euclidean transformation map lines to lines. Indeed, a Euclidean transformation is just a special type of affine transformation. →反転 決まり事 我々は、直線上の鏡影、または円上の反転を意味するために、反転を使う。 以下は、与えられた円に注意して逆元を作図する幾何学的な方法論を与える。 中心c、半径rの円Sの外の点をa、aからSへの2本の折線をa∨p、a∨qとする。さらに、c∨a、p∨qの交点をa’とする。その時、aとa’はSの逆元である。 △cpa’、△capについて、角cは等しく、∠ca’pと∠cpaは直角なので等しい。すなわち、2つの三角形のすべての角は等しい。従って、2つの三角形は相似である。特に、｜→ca｜・｜→ca’｜=｜→cp｜^2=r^2となるような、｜→ca’｜/｜→cp｜=｜→cp｜/｜→ca｜がある。従って、Sはaとa’の逆元である。 最後に、ユークリッド空間とアフィン空間の時の円の反転が特殊な場合を提示して、この節を終わる。 まず、円の反転は、線への写像でないので、アフィン変換ではない。 例）S：円、L：直線Re(z)=2とする。 L上のすべての点が円の外にあり、Sの反転は円の中にある点のLのすべての点の写像である。特に、Lの写像は直線でない。従って、どのアフィン変換においても、線の写像はその線自身なので、アフィン変換において反転は存在しない。 円の反転は、アフィン変換でも、線へ写したユークリッド変換でも、ユークリッド変換にならない。実際に、ユークリッド変換は、アフィン変換の特別な時に限る。 以上です。長いですが、回答よろしくお願いします。
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こんばんは とてもうまく訳されていますね。 私自身がこの文章の数学的な意味をいま一つ理解していませんので、適切なチェックになっていない箇所があるかも知れませんが、微修正させていただいた結果を示します。 →反転 決まり事 我々は、直線上の鏡影、もしくは円上の反転のいずれかの意味で反転という用語を用いる。 以下は、与えられた円に対して逆元を作図する幾何学的な方法論を与える。 中心c、半径rの円Sの外側の点をa、aからSへの2本の接線をa∨p、a∨qとする。また、c∨aとp∨qの交点をa’とする。その時、aとa’はSに関して逆元である。 三角形△cpa’及び△capにおいて、角cは等しく、2つの角∠ca’pと∠cpaはどちらも直角であるため等しい。すなわち、2つの三角形の3つの角はすべて等しい。従って、2つの三角形は相似である。従って、特に、｜→ca｜・｜→ca’｜=｜→cp｜^2=r^2となるような、｜→ca’｜/｜→cp｜=｜→cp｜/｜→ca｜がある。 従って、既に述べたようにSに関して、aとa’は逆元である。 最後に、円における反転（gsb57529さんが訳されたように「円の反転」が正しいのかも知れません。そこは数学的な意味でご判断ください）が、ユークリッド空間やアフィン空間で起こるものとは異なる（難しい？英文は"difficult"となっています）型の変換であることを示してこの節を終わる。 ※このあたりがgsb57529さんの訳と多少異なっています。 まず、円における反転は、直線を直線に変換するものではないため、アフィン変換ではない。 例）S：単位円、L：直線Re(z)=2とする。 L上のすべての点が単位円の外側にあり、従って、Sにおける反転は、L上のすべての点を単位円の内側にある点に写す。特に、Lの写像は直線ではあり得ない。 従って、いかなるアフィン変換においても、線の写像はそれ自身が線であるため、反転はアフィン変換ではあり得ないことになる。 円における反転は、ユークリッド変換でもない。何故ならば、アフィン変換と同様に、ユークリッド変換は線を線に写す。 実際に、ユークリッド変換は、アフィン変換の特別な型に他ならない。 いかがでしょうか？ 数学的な意味合いがおかしくなっていなければ良いのですが。
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8.4.3 Orthogonal Circles An interesting situation to consider is when circles (or lines, or lines and circles) intersect at 90. In any of these cases, the two figures are called orthogonal. In figure 8.9 the circle in the center is surrounded by a set of circles that are orthogonal to it. Since angles are preserved under inversion, what happens if a circle is inverted through another circle to which it is orthogonal? The answer is that the circle is inverted into itself. To see why, remember that the circle of inversion is unchanged by the inversion. The circle orthogonal to it is mapped to a circle that meets it at the same points, and remains orthogonal. Therefore it must be mapped to the same circle. (Note that this does not mean that the points are not moved by the inversionthe ones outside are mapped to points inside and vice-versa, but every point on that circle is inverted to another point on the same circle.)
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(１) Abandon the notion of subject-matter as something fixed and ready-made in itself, outside the child's experience; (２) the various studies, arithmetic, geography, language, botany, etc, are themselves experience- they are that of the race. (３) In the Meiji period, the reformist leader's decision to institute universal primary education and a meritoctatic system gave Japan an educated and trainable workforce and a talented elite at a time when the nation needed to make maximum use of its human resources in its effort to catch up.
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Annibale Carracci’s artwork, The Coronation of the Virgin – 1590-1609, this piece of the soul and the mind. This picture grabbed my attention because it is one of the few paintings in which God, Jesus, and Mary are represented as “equals”, because of their sizes. The arrangement of the figures, and the colors implemented by the artist were other elements that interested me. In the following essay I will discuss the subject matter of the painting, and the technique used, as well as a brief discussion of the features that identify this artwork with the time period when it was painted. In this painting Mary is being crowned by Jesus and God, after her ascension to heaven. This action is taking place in heaven, because angels that are sitting in the background and also clouds closer to the border of the painting surround the three main figures. Jesus, Mary, and God are the main figures. In the center, Mary extends her arms as if welcoming a son/daughter or family member and her face expresses tranquility and acceptance. To her right is Jesus, who lifts His right hand to hold the crown, and His face shows kindness and respect. On Mary’s left, is God, who raises His left hand to hold the other side of the crown that is being placed on Mary’s head. God’s face also shows kindness towards Mary, and as the Father and the Son put the crown on Mary’s head, the Holy Spirit, represented as a dove, descends over her. Crowds of angels sit in order, one on the side of the other, around the semicircular theater in the background of the painting, and others, closer to the viewer’s point of view, are represented playing instruments and holding books, as if they were singing. In the center small human figures are shown, one of them holding a scroll as if they were asking Mary to intercede for them before God. Organization, light, and clothing are important elements of this representation, because they make a reference to the style under which it was created. On “The Coronation of the Virgin,” figures form three triangles. The first and smallest one is formed by Mary’s head and extended arms. Jesus and God’s arms and bellies form the second triangle. The third and biggest triangle starts on the Holy Spirit and extends from both sides to the two low corners of the painting. Triangles may serve as reference to the Holy family and also to the Trinity, which are formed by three figures, the same as triangles have three angles and sides. The organization of the figures in this painting make reference to the High Renaissance where the arrangement of the figures played an important role in the meaning and message that the artist was seeking to convey. This painting is also full of light and color, which bring to this picture a sense of natural appearance, characteristic of the Byzantine and High Renaissance, and also of the Baroque. Clothing is another important element of this painting for it is a reminder of the Classical revival. The colors of the draperies are very basic; blue and pink on Mary’s drapery, white on God and Jesus, and red on two angels in the right corner of the painting, and some green in the center, and a lot of yellow in the background. Another important feature that relates this painting with the style the artist implemented is the body types, especially in Jesus and God. Jesus is shown as having Byzantine facial features, and a classical body type, where muscles and a well shaped body are visible. Also God’s body has been idealized, due to the fact that His body looks as young as His son’s body; giving to this picture a characteristic usually seen during the classical period.
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こんにちは、 英文交じりの質問で申し訳ないのですが、宜しくお願い致します。 隣接角（Adjacent Angles）の定義は知ってます。 そして、隣り合ってる角の合計は１８０ ° まで、と解釈してます。 （Adjacent Angles Two angles are Adjacent if they have a common side and a common vertex (corner point) Adjacent angles add up to 180 degrees.） が、図のaからdまでの角度の合計がa + b + c + d = 360 ° の証明に adj ∠’s at a point sum to 360 °となってるのをみました。 隣接角は１８０度までなのに理解できません。それとも”adj ∠’s at a point sum to 360 °”は間違っているのでしょうか？ どなたか説明して頂けますか？
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シーナ・アイエンガーの「The Art of Choosing」からの英文です。 The desperation of a life in captivity is perhaps conveyed best in Rainer Maria Rilke's poem "The Panther": As the animal "paces in cramped circles, over and over," he seems to perform "a ritual dance around a center/ in which a mighty will stands paralyzed." Unlike the dogs in the Seligman experiment, the panther displays his paralysis not by lying still, but by constantly moving. 【Just like the helpless dogs, however, he cannot see past his confinement. "It seems to him there are / a thousand bars; and behind the bars, no world." Whether the bars are real or metaphorical, when one has no control, it is as if nothing exists beyond the pain of this loss.】 【】の中の英文についてですが、 監禁を通り越して見ることはできない、それは1000のバーがあるようだ。 バーの背後には世界はない。 バーが本当にあるか比喩的にあるとかに関わらず、 人が支配をしないとき、 まるでこの損失の痛みを越えて何も存在しないようである。 というようなことを言っていると思われるのですが、 past his confinement・・・・pastは"通り越して"と訳すのでしょうか？ and behind the bars, no world・・・・ここの意味がよくわかりません。 when one has no control, it is as if nothing exists beyond the pain of this loss・・・・ここの意味もよくとれません。（この損失の痛みを越えて、の部分はどういうことをいっているのでしょう？）
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下記契約文の意味がわかりません ｃとｄの条件の元である契約が成り立つ主旨です この前にａとｂが書かれてました 特に構文とｍａｙの約し方が判りません 何方か約して頂けないでしょうか (c) until the terms of payments under (a) above has been agreed in writing by Ａ and Ｂ, Ｂ may make such payments as are in Ｂ’s reasonable opinion appropriate and upon the agreement being made by Ａ and Ｂ under (a) above, Ａ and Ｂ may settle the balance of payments, and (d) Ｂ need not report to Ａ bases for its royalty payments (where royalty payments are applicable) and if Ａ wishes to confirm correctness of Ｂ’s royalty payments, Ａ may, in principle at its cost, cause a certified public accountant being agreed in writing by Ａ and Ｂ for that purpose to examine and confirm correctness of Ｂ’s royalty payments without such certified public accountant’s disclosing any information obtained by him through his examination.
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The patent system is indeed in the midst of a challenge. Software technology gives us the GPS in our mobile devices, CT scans that provide early health diagnostics, and other wonders, but circumscribing such technologies in a patent is difficult. Advances in genetics and biotech are critically important to treating many diseases and require huge investments that rely on patent protection, but it is often hard to know where the rights of the inventors end and the public's begin.
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8.4.1 Inversion Preserves Angles Between Lines Suppose AB and CD are two lines in the plane that intersect at the point P. If they are inverted in a circle with center O, we will show that the resulting gures make the same angle with each other. The easiest case is if O, the center of inversion, happens to be the same as P. Since both lines pass through the center of inversion, they are transformed into themselves so their images trivially have the same angle between them. If the center of inversion is not on one of the lines (but it may be on the other), then the line that does not contain the center will be inverted to a circle passing throughO. Suppose O is not on AB. Consider the line OX passing throughO that is parallel to AB . Under inversion, OX is transformed transformed into itself (since it passes through the center of inversion), and AB is inverted into a circle K passing through O. Then OX must be tangent to K, since it touches K at O, and if it intersected K in more than one place, OX and AB would intersect, which is impossible since they are parallel. If O is on CD, then CD is inverted to itself, and its angle with OX is clearly unchanged (OX is also inverted into itself). But CD makes the same angle with OX as with AB since they are parallel, so the inverses of AB and CD make the same angle. Finally, if O is on neither line, then both AB and CD are inverted to circles that meet at O, and the lines tangent to those circles at O (OX and OY in the gure) are parallel to the original lines, so they make the same angles as did the original lines.
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It will be seen that we have come full circle in our terminology. By subjecting the phenomenal world to logical criticism, we are left with a clean existential slate; we then create a new and logically consistent reality, and the images which the artist projects to make this reality concrete, the constructions of his imagination and his hands, are the only forms of art which can properly be calles realistic.
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- 次の英文を和訳してください。お願いいたします。
英語が苦手で翻訳ができません。どうかよろしくお願いします。 訳していただく時に下の語句を参照してください。 The Global Positioning System （GPS） enables anyone with a GPS receiver to determine exactly where they are on the Earth’s surface. It is a miracle for anyone who has ever been lost. It is based on 24 satellites nearly 18,000 kilometers above the Earth’s surface, each orbiting the Earth every 12 hours. The way the system works is perhaps easiest to understand in two dimensions. If you ask someone in Hong Kong how far away from them you are and they say that you are 900 kilometers away, you draw a circle 900 kilometers in radius around Hong Kong and know that you are somewhere on that circle. If someone in Manila then tells you that you are 1,200 kilometers away from them, you draw a circle 1,200 kilometers in radius around Manila. This circle intersects the Hong Kong circle at two points, and you know that you must be at one of those points. If someone in Hanoi then says that you are 700 kilometers away, this third circle will intersect with only one of those two points. And this is where you are: in a boat about 200 kilometers off the coast of Vietnam. The same principle works in three dimensions using four centers and four spheres. Your GPS receiver tells you how far it is from four satellites. If it knows exactly where each satellite is, it can tell you exactly where you are. The orbits of the satellites are very predictable and each GPS receiver has the details of where every satellite should be at any given time. The gravitational pull of the sun and moon can alter an orbit very slightly. These changes are monitored by the U.S. Department of Defense and this information is sent via the satellite to the receiver. The distance between the satellite and the receiver is calculated based on the time the satellite signal takes to reach the receiver. This requires the use of very accurate clocks. By fixing a GPS receiver at one spot on the Earth’s surface and taking repeated readings, scientists can tell if that spot is actually moving. The Tsing Ma Bridge in Hong Kong, one of the world’s longest suspension bridges, is built to move with winds and traffic. But too much movement could seriously damage the bridge. Fourteen permanent GPS receivers are attached to various parts of the bridge to record the vertical and horizontal of each part 10 times a second. In Japan, a grid of more than 1,000 GPS receivers has been set up to monitor small, slow movements of the Earth that could provide early warning of an earthquake. Each receiver receives a signal every 30 seconds and can detect movements of less that one centimeter. The GPS was developed by the U.S. military to guide its missiles and bombers to their targets （and to tell its soldiers where they are）. It is now offered free for civilian use. But the European Union is worried that because the GPS is operated by the U.S. military, there may be a conflict between its military and civilian use at some time in the future. So the EU has decided to develop its own system, to commence operations around 2007, to guarantee uninterrupted use by civilians. 【語句】 Global Positioning System （GPS） 「全地球測位システム」 radius 「半球」 Manila 「マニラ」 Hanoi 「ハノイ」 sphere 「球体」 details 「詳細」 the U.S. Department of Defense 「アメリカの国防総省」 Tsing Ma Bridge 「青馬橋」 European Union 「欧州連合 （EU）」
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回答ありがとうございました。 ちなみに、「円における反転」にしました☆・・たぶんそれが合っているみたいなので・・。 「難しい」と「異なる」は、いろいろ調べた結果、「」を採用させていただきました！ いろいろ修正していただいたおかげで、頭の中も整理されて大変勉強になりました。 また、「とてもうまく訳されていますね」とのお言葉、素直に大変うれしかったです。 ありがとうございました。
補足
難しいと異なるのところを入れ忘れました！汗 改めて・・「異なる」を採用させていただきました！ ・・あくまで今のところですが。。。