From One to Many Geometries - Professor Raymond Flood

[@maurocruz1824]

Brilliant! I love these lectures. Greetings from Colombia.

[@damiankofimereku555]

Will advise all maths educator to watch this video and several others from this site. They are very educative

[@NewCalculus]

They are total rubbish. Filled with inaccuracies and infinite stupidity.

[@nagahumanbeingzooofparticl8836]

John Gabriel you are stupid to think of it as stupid.

[@chrisg3030]

The fifth postulate isn't about parallel lines, but about non-parallel lines. Imagine you're standing between two of them stretching into the distance, you know they meet but somewhere too far off to see in which direction they do so, especially with the confounding effect of perspective. No problem says Euclid, you don't even have to move off anywhere, just draw a transversal line where you are and measure the sums of the interior angles. Neat and practical. This is surely the achievement of geometry: how just measuring an angle or two replaces travelling long distances and scaling great heights, whether in land surveying, architecture, astronomy. The fifth postulate is an "element" in that it expresses this utility in its simplest terms. What about the practical import of the other postulates? You might think you've got your ship's mast or astronomical sighting post upright, but walk round it and it turns out to be leaning drunkenly, all right angles have to be equal (4). Keep that landmark at a constant distance from you, and no matter how great that distance you'll come back to where you started (3). You won't go off into the never never, circles don't morph into straight lines or vice versa (2). And first of all, join up the dots, you can't do geometry otherwise (1). Neat and practical.

[@Smile-rd5fn]

Why isn't t history of maths teached in schools?

[@richarddeese1991]

Aha! I wish to tell you of a wonder I have discovered! Behold the joys of harkening to the lectures of one Professor Raymond Flood, master of mathematical verbiage! Thank you. I am truly enjoying these lectures! But I do wonder whether Euclid might not have gotten clean away with it, had he merely *_defined_* parallel lines. For instance: 'Definition: parallel lines are any 2 lines which are equidistant at any and all points perpendicular to each other' [or some such wording.] I also wonder how much it bothered him that the parallel postulate was so obviously more complex than the others. Yet he had to include it in their somewhere! I'm sure we shall never know. At any rate, although I don't have a copy of Euclid's Elements, I *_do_* have a (very old) copy of Robbin's New Plane Geometry. I guess that will have to do - for now! Thanks again, & I'm looking forward to seeing *_all_* of Prof. Flood's wonderful lectures! tavi.

[@ekaratnaacharya5708]

Deductive mathematics is explored by Euclid. How we compare the mathematics before 100 years before and Now? This is my quarry, may we get the date demarcation of South Asian Countries? The matter deliver in this lecture is very interesting and conceptual.And one things How we can classify the phases of history of mathematics? Does we relate the historical relation between Euclid's geometry and Hindu Arabic numbers and their development? So thanks for Prof. Raymond with looking kind cooperation and support with these my interest.

[@NewCalculus]

@31:42 "Spherical geometry does not satisfy the first postulate that of Euclid which says that there is one and only one line connecting any two points." That's news to me. The first requirement (NOT postulate!) of Euclid states that a straight line can be drawn between two points. That's not the same as Flood's nonsensical claim. Euclid didn't ever write "that there is one and only one line connecting any two points". @36 There is no such thing as a "spherical angle". The plane angles are projected onto the spherical triangle.

[@Moronvideos1940]

Spot on.

[@spencerkornelsen8164]

To be fair though, the postulate (ONLY one line) is needed for I.4

[@thedroid3101]

I'm stoopid but you just explained that good

[@sophrapsune]

Thank you very much Prof Flood. 40:58 Saccheri's "very clever" method (it is very clever!), which initially sought to demonstrate the hypothesis of the right angle, is analogous to a method within the Elements itself: it was not novel. Eudoxus is attributed with the method of proof for Elements Book XII, Proposition 2. A similar structure of reasoning is used to prove that the ratio of area for two circles is equal to the ratio of the square of their diameters. Eudoxus succeeded in showing that the inequalities on either side were contradictory, therefore proving the equality indirectly. No doubt this reasoning within the Elements was the inspiration for the eminent geometrician Saccheri's own investigation of the Fifth Postulate. It probably didn't go as Saccheri anticipated, but instead succeeded in discovering non-Euclidean geometries contrary to the Fifth Postulate.

[@Os_Bosniak]

So' In real life the distance between two points isn't a straight line but a curve. Because a -c^2t^2

[@realityversusfiction9960]

EUCLIDEAN DEFINITIONS 1. A point is that which has no part. Oxford English Dictionary. Point: That which in geometry has position but not magnitude, e.g the intersection of two lines Author: If a point has no part, then it can only be due to it being a theoretical point, rather than a linear geometric point of e.g. two lines intersecting (Crossing the other). Given two identical line widths intersecting (crossing) e.g. vertical and horizontal; the intersection point will have an area equal to the square of one line width of their cross section. 2. A line is a breadthless length. For a line to be breadth-less, it has to be a theoretical or an imaginary line such as e.g. the line patterns of star constellations; rather than a transcribed line which has a transcribed area of width, defined by the sharpness of a pencil's point. 3. The extremities of a line are points. The extremities of a line are its two termini (ends) of length; any line other than the line of a differential shape e.g. circle and oval has two termini generally “nominated” as being A to B. 4. A straight line is a line which lies evenly on itself. Linear Geometry A straight geometrically drawn line may be considered to be straight when drawn upon an even straight flat surface. All straight lines of flat surfaces are as with all flat surfaces, finite. Linear Physics A geometrically transcribed line on an even straight flat surface, cannot be considered to be straight below the level of 20 20 vision, or under electron microscope examination. All trajectories of straight line transcribed upon the Earth’s surface are curved over the Earth’s surface. All straight trajectories of e.g. aircraft and missiles travelling above the Earth’s surface are gravitationally curved over the Earth’s surface. The visible three-dimensions of crystalline-based bodies and things do not possess outlines, as their atoms of structure merge directly with the atoms of the surrounding atmosphere. 5. A surface is that which has length and breadth only. Linear geometry A flat surface which has length and breadth is a rectangle or a square. A flat surface possesses a finite area to its shape, shapes possess varied linear angles of length and length of the boundary to their particular shape of the area. A spherical surface is not finite, as it does not have a finite length or breadth Linear physics A surface is not flat below the level of 20 20 vision, or under electron microscope examination 6. The Extremities of a surface are line. The extremities of a surface may be defined by the use of transcribed lines. The extremities of a surface may be defined by varying types of boundary. The extremities of an area of land may be limited by natural features e.g. a cliff edge, an ocean. The extremities of a surface belonging to bodies and things do not possess lines. www.fromthesurfacetothesphere.net

[@AlfaHanen1]

Thanks for his video, nice job, keep ON.,...

[@9340Steve]

Isn't there a contradiction here: At one point he says that, when Saccheri replaced the parallel postulate with the acute angle hypothesis, the result still satisfied Euclid's other axioms. But earlier he says that in sperical geometry two points do NOT uniquely determine a line -- contradicting another one of Euclid's axioms. What am I missing?

[@foobargorch]

I think the first postulate is just regarding the existence of such a line, not about the uniqueness 19:30

[@knutholt3486]

Still you can use Euclidean geometry to describe the surface of a sphere if you describe this surface as n object in a 3-dimmentional space. I am not sure if you can transform all non-Euclidean geometries into an Euclidean one by going up one dimension, but probably you can do it for many. And if you really can transform any geometry into an Euclidean one that way, then the Euclidean geometry is the real geometry, and those others just practical tricks.

[@abstractapproach634]

56:30 forgotten square root?

[@davidwilkie9551]

Geometry is the dominating image.., "encrypting/synced/decrypting -mathematically" or "Holographicly" in QM-Time, substantiated by the density-intensity of least/longest time co-existence duration, in a universe of Relative hyper/sync/hypo spin/reflection. Or.., the rules of counted infinity.., substantiation frequency-amplitude as probability timing-spacing.., relative existence, ..in the Eternity - now spectrum of connection, ..due to the "virtual-holographic " superposition of all rates of timing (= count/counting = "mathematically" calculated self-definition) The first approximation to a point at the 1-0 Central Limit of probability=> self-defining modulation properties that is perfectly spherical/symmetrical because it is exactly the nearest multi-phase limit identity to the point. Ie it's All= infinite multi-phase states in the Eternity-now spectrum relationship inside/outside line of the circumference/boundary of a circle/existence at zero radius. Because the concept of inside/outside is derived from the timed duration of probability, and is the self-defining modulation by wave-envelope/ boundary-> i-reflection of Pi bifurcation, all in the Eternity-now Superposition-point of 1-0 temporal probability-> "virtually distributed" Singularity = Holographic Universe (by the inevitable circular logic of Time Timing/clockwork). Excellent video intro to the geometrical temporal connection principles of relativity. Thank you. _____ Parallel lines "meet at infinite lenght" in the sense that they co-exist here-now, the least-time least "energy" ground-state, transverse-tangential to the Universal Singularity vanishing point. (Mutual equal and opposite orthogonality of Time Timing wave-envelopes?) The constants of natural temporal potential, probability in possibility, occurring at proportionate time rates/curvature, (lensed modulation congruence in temporal Superposition-point Singularity positioning), derive/drive these geometries dynamically, cause-effect, measured-inflated by duration-pulse "self"-instantaneous connectivity => "awareness", modulation-position wave-envelope/probability-path histories, composed at n! => Entanglement, ..Combinations-Permutations sequences of the here-now continuous Quantum principle, ..of prime=time connected discrete-orthogonal multi-phases. "Quantum" means everything is connected This Way!, in mathematical-numbered path/dimensions, distributed and measured as a time rate sequential quality, "mapped in potential positioning" from now to eternity. QM-TIMESPACE All self-defining, consistent geometries begin as the 1-0 Supuerspin Singularity of Time Timing temporal superposition, because e-Pi-i continuous containment, is the symmetrical connection condition of simultaneous substantiation, here-now point, and infinite out-there spacing, of Eternity-now. After recognizing that the Universe is a Hologram of pure relative motion, time duration frequency density and amplitude intensity, I know understand why those who also observed this state of the real image of Time accused more practical techniques using languages of mechanical symbols, ..of practicing "Black (sooty) Arts in Magic" and Mystery Religions embellished with the more imaginative kind of speculation and exaggerated assumptions that are plausible until tested by the Scientific Method. Unless you have a rational and reasonable comprehension of QM-Time, no-thing makes sense because quantum dualism is inherently multi-phase ambiguity. Any observable aspect of the Universe is substantiated in the time duration spectrum of existence by a relative degree/probability of the Time Timing QM-Time Principle/function.., the axial-tangential, = Quantum Operator, e-Pi-i occurrence-> interference positioning backed by pulses within pulses to Infinity Mathematical Geometrical Existence) "Right", and every other possibility of potential/virtual approach to omnipresent connection now, is the aspect of Infinity in the QM-TIMESPACE Singularity positioning, distributed/projected/drawn/radiated/inflated +/- , by the Exclusion +/- Principle at the Unique Central Limit 1-0D coordination by Polar-Cartesian connection.., which continuous temporal inflation potential "flow" conducted by the integrated occurrence of primes and cofactors, implies "holographic" fractal-symmetrical "numberness" radiation.

[@bencheesecake8795]

Reminds me of timecube, nonsense of highest order

[@Kurtlane]

Huh?

[@dorothyhyder1486]

Just learning of Euclid. I have already given my Family the name DuckyDuckEuclid

[@ichhabedich1]

sehr schöne sprech hier

[@Moronvideos1940]

Uh, how come a lot of these guys have Mickey Mouse voices. Just an observation ....

[@mamathamanu4239]

Intalegent