Instead, he notes that Richardson's empirical law is compatible with the idea that geographic curves, such as coastlines, can be modelled by random self-similar figures of fractional dimension.

They expanded the range of geometry to many new kinds of figures, curves, surfaces, and solids ; they changed its methodology from trial-and-error to logical deduction ; they recognized that geometry studies " eternal forms ", or abstractions, of which physical objects are only approximations ; and they developed the idea of the " axiomatic method ", still in use today.

The cusp form idea came out of the cusps on modular curves but also had a meaning visible in spectral theory as ' discrete spectrum ', contrasted with the ' continuous spectrum ' from Eisenstein series.

The more strict analogy expressed by the ' global field ' idea, in which a Riemann surface's aspect as algebraic curve is mapped to curves defined over a finite field, was built up during the 1930s, culminating in the Riemann hypothesis for local zeta-functions settled by André Weil in 1940.

In geometry, the notion of a connection makes precise the idea of transporting data along a curve or family of curves in a parallel and consistent manner.

The idea goes back to earlier work of Hurwitz, who treated algebraic correspondences between modular curves which realise some individual Hecke operators.

In 1998, Frey proposed the idea of Weil Descent Attack for elliptic curves over finite fields with composite degree.

Later, in 1686, when Newton's ' Principia ' had been presented to the Royal Society, Hooke claimed from this correspondence the credit for some of Newton's content in the ' Principia ', and said Newton owed the idea of an inverse-square law of attraction to him – although at the same time, Hooke disclaimed any credit for the curves and trajectories that Newton had demonstrated on the basis of the inverse square law.

`` It was Brenner's idea '', Jess mumbled, dabbing at his nose.

He had no idea which was up and which was down.

Beyond the two basic tasks mentioned above, no attention was paid by statesman or scholar to an idea of state responsibility, either internally or externally.

Despite the clarity of his presentation, his idea was not of Einsteinian calibre.

To get an idea of the embarrassment and chagrin that was heaped upon Wright and Olgivanna, we should bear in mind that the raids were sometimes led by Miriam in person.

Apparently still sensitive about the idea with which General Gates had approached him at Saratoga, namely, that George Washington be replaced, Morgan was vehement in his support of the commander-in-chief during the campaign around Philadelphia.

Their policy ran counter to the traditional idea that a good fighter was usually a libertine, and that in sex affairs `` God-given passion '' was a proof of manliness.

Yet, the idea imbedded in each was identical: to surround the unknown with mystery and to isolate that class which had been given special dominion over the secrets of God.

The idea was not even suggested because political expediency prevailed over wisdom.

He had no idea where he was.

He realized that he had no idea where the telephone was.

Although Mr. Brown was not himself its inventor ( it was a French idea ), it is typical that his intuition first conceived the importance of mass producing this basic tool for general use.

While Mr. Blatz was putting up the pegboards and starting the workbench, Mr. Crombie told him of this idea about paneling the whole end of the cellar.

Instructions to relax, i.e., to be `` spontaneous '', and react immediately to whatever impulse they might have, was not sufficiently reassuring until some idea of the possibilities of normal reactions had been given.

By this time Churchill was not so cordial toward moving Poland westward as he had been at Teheran, where he and Eden had both heartily approved the idea.

The dated poems also give us an idea of the degree to which Hardy drew upon past productions for his various volumes, and therefore probably are an indication of the amount of poetry he was writing at the time.

For weeks he had been saying that Hudson's idea of sailing through to Java was absurd.

And it was Lucy Upton who first started the idea of a regular course in Music at Spelman College.

That, incidentally, might give you some idea of what Felix was like.

Well, it hadn't been what it seemed, he'd had no idea the girl was in there.

This was senseless -- he had no idea what to look for.

`` I'll get my references in order '', Needham said, and though he spoke with a smile, Casey somehow got the idea that he was not particularly amused.

Even before his mind had rounded out the idea, he thrust one hand into his trousers pocket and pulled out the six slugs he had taken from the revolver.

In 1899, the Japanese government passed an act labeling the Ainu as former aborigines, with the idea they would assimilate — this resulted in the land the Ainu people lived on being taken by the Japanese government, and was from then on under Japanese control.

When a hypothetical dilemma was given to 24 people and according to the dilemma they had the capability of pushing a stranger in front of a train so they could rescue five people, individuals who had taken selective serotonin reuptake inhibitors were not as likely to support the idea of pushing the person.

Everything a new colony might need had to be taken, since Phillip had no real idea of what he might find when he got there.

In them he concentrated on the idea that prophetic inspiration was possible even in post-Talmudic times, and, indeed, had taken place at various times and in various schools, from the Geonim to Maimonides and beyond.

At the end of the work, Bede added a brief autobiographical note ; this was an idea taken from Gregory of Tours ' earlier History of the Franks.

" Four normal distribution | Gaussian distributions in statisticsThis unproved statement put a strain on his relationship with János Bolyai ( who thought that Gauss was " stealing " his idea ), but it is now generally taken at face value.

This idea was taken up strongly in the training of Beaux-Arts architecture, ca 1875-1915: see architecture parlante.

The concept was much improved by the Italian Roberto Valturio in 1463, who devised a boat with five sets, where the parallel cranks are all joined to a single power source by one connecting-rod, an idea also taken up by his compatriot Francesco di Giorgio.

Critics, such as psychiatrist Niall McLaren, argue that the DSM lacks validity because it has no relation to an agreed scientific model of mental disorder and therefore the decisions taken about its categories ( or even the question of categories versus dimensions ) were not scientific ones ; and that it lacks reliability partly because different diagnoses share many criteria, and what appear to be different criteria are often just rewordings of the same idea, meaning that the decision to allocate one diagnosis or another to a patient is to some extent a matter of personal prejudice.

The idea of a relation between the language of the Aegean Linear scripts was taken into consideration as the main hypothesis by Michael Ventris before discovering that in fact the language behind the more modern Linear B script was Mycenean, a Greek dialect.

A new idea taken over from still photography was " soft focus ".

The enhanced idea gained Eiffel's support for the project, and he bought the rights to the patent on the design which Koechlin, Nougier and Sauvestre had taken out.

A further step was taken by the idea of the Shaktis.

Part of his proposal was the idea that micropayments could be automatically exacted from the reader for all the text, no matter how many snippets of content are taken from various places.

In an example taken from his high school experience, Miller recalls that one of his classmates ... struck upon the brilliant idea of using an old, broken mousetrap as a spitball catapult, and it worked brilliantly .... It had worked perfectly as something other than a mousetrap .... my rowdy friend had pulled a couple of parts -- probably the hold-down bar and catch -- off the trap to make it easier to conceal and more effective as a catapult ... the base, the spring, and the hammer.

Brabham records that he was not taken with the idea of driving, being convinced that the drivers " were all lunatics " but he agreed to build a car with Schonberg.

The idea was taken up by Latin American intellectuals and political leaders of the mid-and late-nineteenth century, who no longer looked to Spain or Portugal as cultural models, but rather to France.

Industrial democracy refers to the same idea, but taken much further.

He speculated that myths arose due to the lack of abstract nouns and neuter gender in ancient languages: anthropomorphic figures of speech, necessary in such languages, were eventually taken literally, leading to the idea that natural phenomena were conscious beings, gods.

Born's idea was soon taken over by Niels Bohr in Copenhagen who then became the " father " of the Copenhagen interpretation of quantum mechanics.

These results would seem inconsistent with the idea of short-term memory as the distractor items would have taken the place of some of the word-pairs in the buffer, thereby weakening the associated strength of the items in long-term memory.

It was an idea later taken up by British administrators such as Herbert Hope Risley but remains disputed today.

Modern uses of the word " theory " are derived from the original definition, but have taken on new shades of meaning, still based on the idea that a theory is a thoughtful and rational explanation of the general nature of things.