The detailed geometry of the coenzyme molecule as a whole is fascinating in its complexity.
Analytical geometry has never existed. There are only people who do linear geometry badly, by taking coordinates, and they call this analytical geometry. Out with them!
I love making object form; I wish I was doing more of it. I admire the research of my colleagues, and sometimes it makes me sad when their beautiful work - the deep dives into formal research and nuances of geometry and so on - ends up circling in more and more circumscribed contexts. I wish they were more powerful. It's not a modern proposition. Active form doesn't kill object form. I want my students to have all those skills related to geometry, shape, measure, scale, etc. , plus skills for using space to manipulate power in the world.
Geometry is one of the handles of science and philosophy.
He is not a true man of science who does not bring some sympathy to his studies, and expect to learn something by behavior as well as by application. It is childish to rest in the discovery of mere coincidences, or of partial and extraneous laws. The study of geometry is a petty and idle exercise of the mind, if it is applied to no larger system than the starry one. Mathematics should be mixed not only with physics but with ethics; that is mixed mathematics. The fact which interests us most is the life of the naturalist. The purest science is still biographical.
Seriously, you don't have to know English. It'd be nice, a nice little plus. We don't want miracles. You don't have to know the country's language. But just some shapes, that's all. A square. A little geometry.
We come now to the question: what is a priori certain or necessary, respectively in geometry (doctrine of space) or its foundations? Formerly we thought everything; nowadays we think nothing. Already the distance-concept is logically arbitrary; there need be no things that correspond to it, even approximately.
Projective geometry is all geometry.
There is no need to express art in terms of nature. It can perfectly well be expressed in terms of geometry and the exact sciences.
Every one who understands the subject will agree that even the basis on which the scientific explanation of nature rests is intelligible only to those who have learned at least the elements of the differential and integral calculus, as well as analytical geometry.
There is still a difference between something and nothing, but it is purely geometrical and there is nothing behind the geometry.
Poetry is as precise a thing as geometry.
You must follow me carefully. I shall have to controvert one or two ideas that are almost universally accepted. The geometry, for instance, they taught you at school is founded on a misconception.
The first test of potential in mathematics is whether you can get anything out of geometry.
Not that the propositions of geometry are only approximately true, but that they remain absolutely true in regard to that Euclidean space which has been so long regarded as being the physical space of our experience.
The purely formal language of geometry describes adequately the reality of space. We might say, in this sense, that geometry is successful magic. I should like to state a converse: is not all magic, to the extent that it is successful, geometry?
Geometry existed before creation.
Geometry is the archetype of the beauty of the world.
Scientists say every action initiates an equal and opposite reaction. I say that's just the start. I say every action initiates a most unequal and upredictable chain reaction, that every filament of living becomes part of a larger weave, while remaining identifiable. That every line of latitude requires several stripes of longitude to obtain meaning. That every universe is part of a bigger heaven, a heaven of rhythm and geometry, where a heartbeat is the apex of a triangle.
The opinions of men should not be the object of any government. Our civil rights are no more dependent on our religious beliefs than they are dependent upon our thoughts about geometry or physics!