Jim Simons
Jim Simons
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Ancient Spherical Trigonometry
We delve into the past to see how ancient astronomers used spherical trigonometry, using Menelaus's theorem, a result very different from the spherical sine and cosine rules of modern spherical trigonometry. They used spherical polar co-ordinates some 5000 years before Descartes introduced Cartesian coordinates! Lots of interesting and and history.
มุมมอง: 177

วีดีโอ

Rolling One Coin Round Another
มุมมอง 4119 ชั่วโมงที่ผ่านมา
A problem that's been doing the rounds for 40 years or so. You have a little coin and a bigger one ith three time the radius, and yoi roll the little one round the bidgone, How many times does it rotate as it rolls?
Spherical Trigonometry
มุมมอง 10428 วันที่ผ่านมา
The fifth part of my series on trigonometry and its history, this deals with spherical trigonometry as it has been for the last 1000 years. (A later video with deal with the previous 1000 years). We start by exploring the geometry of the sphere, comparing and contrasting it with the plane. This includes one of my FAVOURITE THEOREMS in all of mathematics. Then we cover trigonometry in spherical ...
Subtracting Left to Right
มุมมอง 2062 หลายเดือนก่อน
I teach you how to subtract two multi-digit numbers working from the left to the right. You might think that is impossible, but watch! If you learn this method and practice a little, I think you will find it easier than the standard right-to-left method. I also think it makes it easier to understand WHY the answer is what it is. What'd not to like?
From Cubics to Complex Numbers
มุมมอง 3537 หลายเดือนก่อน
We all know the formula for solving quadratics, but there is also a formula for solving cubics. It's a pretty piece of mathematics, and its discovery, in the sixteenth century, is thought by many to be the start of modern mathematics, because it sowed the seed that led to complex numbers. In this video I show how to solve cubic equations, and follow the story of the development of complex numbers.
Trigonometry and its History IV: Prosthapaeresis, the First Fast Multiplication Algorithm
มุมมอง 2029 หลายเดือนก่อน
I explain phrosthaphaeresis, a method for rapid multiplication that was invented in the sixteenth century, and was used before logarithms superceded it at the start of the seventeenth century. It uses ideas from trigonometry that go back to Ptolemy of Alexandria in the second century. I then time it, comparing it with ordinary multiplication and with logarithms, for 4-figure multiplication and ...
Trigomometry and Its History III - Trigonometry Meets Calculus and They Make Waves
มุมมอง 137ปีที่แล้ว
We leave angles, and indeed geometry, behind, as Sin and Cos become waves - usually functions of time rather than an angle. Along the way we develop the theory with slightly more rigour than school text books usually do, and as usual explore the history of these ideas.
Trigonometry and Its History II - Obtuse Angles and the Curious History of the Cosine Rule
มุมมอง 189ปีที่แล้ว
I talk about how I like to develop trigonometry, give some of my favourite proofs, and explore the history. The history of the sine rule is simple - it' over 1300 years old. The cosine rule took much longer and was only fully formed some 200 years ago. I explore why that is.
Babylonian Mathematics
มุมมอง 1.7Kปีที่แล้ว
A short look at the extraordinary mathematics of Ancient Babylon, from nearly 4000 ago. We see their base 60 number system and some of the things they could do with it. At the end we examine the amazing clay spreadsheet that is Plimpton 322, which is a sort of precursor of trigonometry.
Trigonometry and its History - 1. right angled triangles
มุมมอง 443ปีที่แล้ว
Aiming for enrichment of school mathematics, I tell the history of elementary trig from ancient Greece to India, and back to Europe. We meet a Babylonian spreadsheet all about Pythagoras's theorem, well over 1000 years before Pythagoras. We find that the first trigonometry didn't have right angled triangles at all, but only a circle and a chord. I tell the mysterious story of how sine got its n...
Tidal Destruction
มุมมอง 672 ปีที่แล้ว
The forces that cause the tides and slow the moon down, can also destroy things, fir example grinding up comets to create Saturn's rings. We lok at how that works
Tidal Locking
มุมมอง 1022 ปีที่แล้ว
The forces that cause the tides have also caused the moon's spin to slow right down so that it always show us the same face. We'll look at how that works, and also see why Mercury's day is twice as long as its year, a curious phenomenon caused again by tidal forces
How the tides work in the oceans
มุมมอง 1592 ปีที่แล้ว
Many of the explanations of the tides are wrong, and even when they are right they are nevertheless misleading. This video does it right, and that requires some mathematics.
Three pretty geometric theorems, proved by complex numbers
มุมมอง 27K2 ปีที่แล้ว
Bottema'a theorem, van Aubel's theorem and Napoleon's theorem, are all brilliant. If you have never seen them before, you will be amazed! I prove then all by working in the complex plan, as van Aubel did in 1878.
Modular Arithmetic Part Two - A Tale of Two Triangles and the Chinese Remainder Theorem
มุมมอง 1322 ปีที่แล้ว
A follow-on from my previous video, "Modular Arithmetic and Checksums". This video explores some more ideas using modular arithmetic, including a surprising connections between two famous triangles, and the famous and ancient Chinese Remainder Theorem
Sundials and the Equation of Time
มุมมอง 7K2 ปีที่แล้ว
Sundials and the Equation of Time
Modular Arithmetic and Checksums Part One
มุมมอง 4813 ปีที่แล้ว
Modular Arithmetic and Checksums Part One
How We Used Log Tables
มุมมอง 9493 ปีที่แล้ว
How We Used Log Tables
Generalising Pythagoras
มุมมอง 2613 ปีที่แล้ว
Generalising Pythagoras
Why is a^(½)= √a?
มุมมอง 3263 ปีที่แล้ว
Why is a^(½)= √a?
The Chain Rule - How to REALLY Understand It
มุมมอง 8423 ปีที่แล้ว
The Chain Rule - How to REALLY Understand It
1d vectors
มุมมอง 1883 ปีที่แล้ว
1d vectors
Graph transformations beyond your dreams
มุมมอง 1273 ปีที่แล้ว
Graph transformations beyond your dreams
Graph Transformations
มุมมอง 2313 ปีที่แล้ว
Graph Transformations