Best exploration books according to redditors

It's difficult to answer this, given that no-one who lived in a period where they were doing anything like accurate cartography believed in a flat earth. The idea that people in the Middle Ages believed in a flat earth is a myth invented in the nineteenth century - see Jeffrey Burton Russell's Inventing the Flat Earth: Columbus and Modern Historians (1991)

So early cartographers were well aware that the earth was round and never had to deal with the problems involved with trying to make maps on the assumption it was flat.

First came the size of the Earth. That was done around 240 BC by Eratosthenes.

Then a whole lotta nothing happened till Kepler who figured out some rough orbits for planets that was proportional, but didn't have exact figures. But he did have the P^2 = a^3 thing going which was cool since it meant if we could get the orbital distance from the Sun for one planet, we could standardize the formula and make it work for all planets.

Then Newton came along and tweaked Kelper's 3rd law by noting it wasn't quite that simple because masses of the objects mattered. But barely since the Sun is so much more massive.

Then in the late 1700's, Venus was set to transit the Sun a few times. By observing the transit from different points on Earth, astronomers were able to use parallax to determine the exact distance to Venus and the Sun. By 1771, French astronomer Jérôme Lalande had come up with the distance to the Sun being off by only 2%. (Good book on the topic)

Once we knew the Earth-Sun distance, we could again use parallax to get distances to nearby stars by observing them when Earth was in different parts of its orbit for a long baseline. The hardest part was knowing which stars to choose as a target since many stars don't show much as they're far away. At the time, many astronomers thought all stars were the same intrinsic brightness and therefore, brighter ones must be closer. Turns out not so much. Ultimately, the first successful attempt was in 1838 for 61 Cygni. Several others followed soon afterwards. (Another book on that topic)

This is a long answer, but you need to know a bit of the history of astronomy to understand how astronomers figured out how to calculate the distances to stars. Astronomy is the oldest science there is. It goes back to the most ancient civilizations, the Messpotamians were looking up at the sky and studying it. Even they noticed that the stars were not all there was. The stars themselves, sure, lots and lots of dots. But there are also 5 planets, the sun and the moon and all of those things move across the sky as time passes. The stars all moved together, but the planets were different. They didn't follow the same path across the sky as the stars did.

Ancient thinkers like Aristarchus and Eratosthenes calculated surprisingly accurately the circumference of the earth and the scale between the earth, the moon and the sun. The used measurements from lunar and solar eclipses, geometry, etc to make really, really good estimates for the time.

In the 1400's or so, attempts to understand what we saw in the sky were made by people like Johannes Kepler. He saw the sky as layers of geometric shapes or crystal like... things, that rotated around the earth. A model he build looked like this with earth in the center, the sun above it, the moon above that, mars above that and so on until you got to the stars which was the biggest enclosure. He tried for many years to figure out why mars retrograded, that it appeared to stop, move backwards, stop, then move forwards again over time in the sky. He eventually figured out that it was because the planets didn't move in perfect circles like people thought, but that they moved in elipses or ovals

Nicolaus Copernicus was one of the first to propose that the earth revolved around the sun, and not the other way around, using what Kepler figured out which was that the planets do not move in circles, but elipses (ovals).

Galileo Galelie with an understanding of Keplers and Copernicus' work was the first person to point a telescope (invented a few years earlier by someone else) at Jupiter in the sky. He discovered that Jupiter had 4 moons that orbited around it and he could observe and measure it. This was further proof that the earth went around the sun and not the other way around.

There are also sometimes rare events, which give us invaluable information used to calculate astronomical distances. One such event being a transit. That's when one of the planets close to the sun, Mercury or Venus, passes in front of the sun from earths point of view. Here it is in 2012 Astronomers could use this information to calculate the distances to the planets, and determine the size of the solar system. In 1761 and 1769 Hundreds of scientists from all across the world planned for the transit. Some traveled half way across the world, not an easy feat in the 1700's to get the data. Then they all collaborated it (which took years) and this gave us a much better understanding of the size of the solar system and the distances involved.

In the late 1700's William Herschel and Charles Messier were cataloguing stars and nebula. It turns out that what looks like just dots with the naked eye have a lot of differences when viewed through a telescope. Some are brighter, some dimmer, some are bigger, some are smaller and even some of different colors. Many stars will also fluctuate in how bright or dim they are over time, like a very slow pulse. It also turned out there were objects that weren't stars in the sky. But they were too dim to see with the naked eye and only visible in a telescope. Messier cataloged over 100 galaxies and nebula and produced a guide still used today. The telescope also enabled astronomers to figure out that there weren't about 5000 or so stars that we could see with the naked eye, as everyone in history before then thought, but that there were millions upon millions (and as telescopes got better, billions upon billions) of other stars, too dim to see with the naked eye. All this can be measured, recorded, compared and calculated. The invention of the telescope gave astronomers lots and lots (and lots and lots) of data to work with.

Here's where we get to the specific of your question.

In the late 1800's Henrietta Leavitt employed as a "computer" (someone who just "computes", or records, analyses and does the math of data collected about stars) discovered the relation between the luminosity and the period of Cepheid variable stars. She figured out how to determine the distance to astronomical objects. First calculating the Large & Small Magellanic Cloud, two small galaxies outside that were thought to be just clouds of dust.

Edwin Hubble, namesake of the Hubble Telescope used Leavitt's data and method to figure out that the universe was expanding, by measuring the redshift of galaxies outside our own. This was the biggest step towards the big bang model of the universe.

These are only really the top names and discoveries. Many scientists during all that, and up until now have worked together to figure out how to determine the size of a star, what the stars are made of, how they work and what they actually are, and how to figure out how far apart all those little dots are.

But what we know about the universe today is everything learned in many fields across lots and lots of time. If you're really interested in a great "history of science, what we know and how we know it" I'd recommend A Short History Of Nearly Everthing by Bill Bryson. It does a great job of explaining all this and more in easy to understand laymen terms.

I would read Empire of the Stars for a poignant tale of how this can happen even among the most brilliant of scientific minds.

I think @omeow gives a good answer. Not less calculus as Calculus is the bedrock of so many different areas of maths and science. If you want a good book on this Steve Strogatz's lastes "infinite powers" is awesome: https://www.amazon.co.uk/Infinite-Powers-Calculus-Reveals-Universe/dp/1328879984

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That said, statistics is becoming increasingly important. We need to train everyone, not just Maths grads in more stats. I think if you want to guaruntee a job coming out of an undergraduate degree then Stats is a pretty good bet. Also if you're looking for a primer on stats then David Spiegelhalter's book "The art of statistics" iss a great one: https://www.amazon.co.uk/Art-Statistics-Learning-Pelican-Books/dp/0241398630/ref=sr_1_1?keywords=the+art+of+statistics&qid=1569697929&s=books&sr=1-1

It certainly wasn't. There are two primary reasons why we taught this in grade school:

First, a work of historical fiction by Washington Irving about Christopher Columbus became confused by many as a work of historical fact, due in large part to it being one of the first attempts at historical fiction in America. In the book, Columbus is portrayed heroically, believing that the world is round, and being set upon from all sides by the popular wisdom that the world was flat. In reality, people knew the world was round, and indeed knew the circumference of it as well. Columbus was convinced that the Earth was a much smaller sphere than had been calculated, and had North America not been in the way, Columbus and his entire crew would have perished long before they reached India, having carried with them only enough supplies to go the distance Columbus believed needed to reach it.

Second, the work of John William Draper, Andrew Dickson White, and others on their debunked "conflict theory" helped fuel the idea. Draper and White believed that science and religion had always been opposed, and had no ethical qualms making stuff up to make people who lived prior to the scientific revolution to make them look stupid - uneducated pawns under the thumb of the Church of Rome. Attitudes in the scientific community at the time were all too happy to swallow this tripe whole.

http://www.amazon.com/Inventing-Flat-Earth-Columbus-Historians/dp/027595904X/ref=sr_1_1?ie=UTF8&qid=1454081274&sr=8-1&keywords=Inventing+the+Flat+Earth#reader_027595904X

If you're interested in Calculus, Steven Strogatz just wrote a book called Infinite Powers which goes through the historical development of the concepts starting from the Greeks. He gives detailed explanations of methods used by Archimedes to "prove" concepts, or at least to gain intuition about certain questions before formalizing them, and then walks through their development over the years. It's written to be accessible for non-mathematicians but it certainly not one of those pop-science books that just deals with over-simplified explanations of very high-level ideas.

There are two well done books on the topic Inventing the Flat Earth: Columbus and Modern Historians and Flat Earth The History of an Infamous Idea. The first traces how the notion that medievals didn't know the Earth was round came about (it was invented in the 19th century by people like the above mentioned Washington Irving and then truly popularized in anti-religious tracts which emerged in the debates over Evolution), while the latter looks at the notion that the Earth was flat, it's demise in antiquity, and the resurrection of the idea among Flat Earth societies in the 19th century.

I think your students will be lucky to have a teacher who is so excited to teach them! There's a lot to say here, so I'll just add a couple of points to the discussion.

TIP 1: A BOOK

Steven Strogatz (Cornell math professor and renowned mathematical expositor) has recently come out with a new book called Infinite Powers: How Calculus Reveals the Secrets of the Universe. I haven't read it yet, but based on what I know about it, I suspect you'd find a ton of inspiration from this.

TIP 2: A CONCEPTUAL FRAMEWORK

General framework

Students can easily be overwhelmed by the technical aspects of the subject, but everything we do in calculus can be contextualized via a simple (but brilliant) framework.

(This is something I emphasize in my tutoring, but you might find it helpful when planning classroom lessons as well. One option might be to open the course with a brief overview of calculus based around this framework, perhaps in the first class. Then, each time a new idea is introduced, it can be placed within the framework that you established at the outset.)

1. Approximations (approximate difficult nonlinear problems by easy linear ones)
   
2. Limits (refine your approximations until infinity turns them into exact values)
   
3. Shortcuts (develop systematic shortcuts for calculating important limits)
   
   Approximations, and something close to the idea of a limit, were put to use in ancient Greece (see the work of Archimedes). Thousands of years passed before the third stage was developed and calculus came to fruition - for that, we needed the analytic geometry of Descartes and Fermat.
   
   Altogether, this framework enables us to turn difficult problems about changing quantities into easy problems about geometric quantities. Let's see how this plays out in the two main branches of the subject.
   
   Differential Calculus
   
   The central problem is to find the rate at which a given quantity is changing (with endless applications). We can reframe this as a question about slope. How can we find the slope of a nonlinear curve? For example, how could we find the slope of the parabola y=x\^2 at (3, 9)? This is not obvious at all, but calculus makes it easy, as follows.
   
   
4. We only know how to find the slopes of lines, so let's draw a line that appears to have the same slope as the parabola (the tangent line). Can we find its slope? We'd need two points, but the only point on the line that we know for sure is (3, 9). It seems we're stuck, but we won't give up! Instead, we'll approximate by a secant line.
   
5. We can improve our approximations and watch to see which value they approach... They're approaching 6. We call this the limit, and it must be the answer!
   
6. That was a lot of work. Can we find a shortcut? Whether we use (3, 9) or (4, 16), the process should be the same. Instead of repeating it every time we use a different point, is there a way we could represent multiple values at the same time? Algebra to the rescue. We can use (x, x\^2) as a placeholder. After a little algebra, we get that the slope is 2x. So, what's the slope at (4, 16)? This problem is now as easy as multiplying by 2: 2*4 = 8. From here, we can do something similar for other basic functions (power functions, exponential functions and logarithms, trig. functions and inverse trig. functions) as well as combinations of those functions (sums, products, compositions), and then we'll have shortcuts for all the functions of precalculus.
   
   Integral Calculus
   
   The central problem is to find the accumulated change in a continuously changing quantity. We can reframe this as a question about area! (This can be motivated by considering speed vs. distance.) How can we find the area of a curved (nonlinear) shape? For example, how could we find the area underneath the parabola y=x\^2 between x=0 and x=3?
   
   
7. Apart from the circle (whose area was determined by methods similar to the methods of calculus), we only know how to find the areas of shapes whose sides are straight line segments (like triangles, rectangles...). When it comes to finding areas, the simplest of these shapes is the rectangle, so let's approximate using rectangles.
   
8. We can improve our approximations and watch to see which value they approach... They're approaching 9. We call this the limit, and it must be the answer!
   
9. That was a lot of work. Can we find a shortcut? Here, the fundamental theorem of calculus is the shortcut we're looking for. We can apply it once we build up an inventory of antiderivative formulas for important functions.
   
   Applications
   
   As an example, consider solids of revolution.
   
   
10. Choose an approximating element (e.g. a disk or a shell). Approximate by summing the volumes of these elements.
    
11. Take the limit, so the sum becomes an integral.
    
12. Evaluate the integral using a shortcut (the fundamental theorem of calculus).
    
    That's the idea. I hope it helps!
    
    Edit: Included extra language to clarify the bit about approximating by rectangles.

Is the question "Why is calculus considered so important?"

If so, I would say the reason comes down to what Calculus is capable of. It is, at its core, a language for describing how things change. It also provides a set of intuitions about how things change which is critical for almost any area of applied science and mathematics.

3blue1brown recommended a book recently that I've been reading which makes these points better than I can called Infinite Powers. I highly recommend it if you'd like to gain more inspiration around the importance and wonder that Calculus presents. It's a very easy and quick read.

Edit: rereading your question, maybe you're asking "why is it dis-proportionally represented in the US when compared to the UK?" ; my doesn't really help there, but I'd still stand by the book recommendation!

Link

The historians of ideas know that science was born in medium infused with Christian ideas and the Dark ages weren`t so dark.

Link

I find that science history and biography gives a good understanding of scientific methods, and when written for the lay-person, doesn't get so bogged down in technical jargon.

Here are a few of my favorites:

• A Short History of Nearly Everything - Bill Bryson
  
• Chaos: Making a New Science - James Gleick
  (Also check out his biographies of Isaac Newton and Richard Feynman)
  
• Stiff: The Curious Lives of Human Cadavers - Mary Roach
  
  And here are a few on my to read list:
  
  
• Seeing Further: The Story of Science, Discovery, and the Genius of the Royal Society - Bill Bryson
  
• Sapiens: A Brief History of Humankind - Yuval Noah Harari
  
• The Butchering Art: Joseph Lister's Quest to Transform the Grisly World of Victorian Medicine - Lindsey Fitzharris
  
• Rabid: A Cultural History of the World's Most Diabolical Virus - Bill Wasik & Monica Murphy
  
• The Wild Trees: A Story of Passion and Daring - Richard Preston
  
• The Age of Wonder: How the Romantic Generation Discovered the Beauty and Terror of Science - Richard Holmes
  
• The Invention of Science: A New History of the Scientific Revolution - David Wootton
  
  I hope that helps.

This is apparently based on the vanity press musings of a Romanian conspiracy theorist from 2009.

Here are some books about astronomy. (Not how-to on astronomy)

Coming of Age In The Milky Way

Chasing Venus

The Hole In The Universe

Atom

Miss Leavitts Stars

Pale Blue Dot Sequel to the original book, Cosmos.

Death By Black Hole

Watching this made me think of the book “The Day the World Discovered the Sun”, and how multinational scientific expeditions were launched and people died in the process of measuring the transit of Venus, and now here I am in my kitchen stuffing my mouth with a bagel while I watch a dot float across a yellow ball on my phone.

https://www.amazon.com/dp/0306820382/ref=cm_sw_r_cp_api_i_IbS2Db3GM0XT6

If you are interested in this surprisingly fascinating topic, check out You Are Here: From the Compass to GPS, the History and Future of How We Find Ourselves.

I highly recommend reading about his adventures firsthand. He published all of his travel journals and they are in the public domain. You can find them on Amazon or various print-on-demand kiosks. Fascinating reads, but some portions help if you Google locations to translate the areas he is talking about with the modern names. They read half like adventure stories and half like botanical notebooks.

A few months ago I gave a presentation at a local library about the history of tea, which of course included talking about Robert Fortune's adventures. Afterward an old man approached me with a grin on his face. He handed me his driver's license -- his name was Robert Fortune. It made his day to know someone famous shared his name; he had never heard of the Robert "The Tea Thief" Fortune before.

Arctic Explorations

> Historia Verdadera de la Conquista de la Nueva España y ahí de Bernal Díaz del Castillo

Edición: Link de amazon.

Neutral Buoyancy

https://www.amazon.com/Neutral-Buoyancy-Adventures-Liquid-World/dp/0802139078

Here are all the local Amazon links I could find:


amazon.com

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amazon.ca

amazon.com.au

amazon.in

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amazon.de

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> At the core of this book is a linguistic argument: that the emergence of these words in the 16th and 17th centuries proves that significantly new ideas had emerged. Wootton puts forward a very strong version of this thesis.

> (...)

> Overall, Wootton justifies nicely his argument that we “tend to overestimate the importance of new technology and underestimate the rate of production and the impact of new intellectual tools”.

> (...)

> The Invention of Science is not only a history of science but a revisionist historiography of science, in which Wootton attacks allegedly homogeneous schools called “the sociologists of science” and “the cultural determinists”, expending thousands of testy words situating himself carefully between two implausible views, the extreme versions of which are held by almost no one.

Amazon link.

It's not an either/or.

Maybe take a small dose of little book called Inventing the flat earth, and consider why you think they're opposed.

I'm late to the game on this thread however Remarkable Creatures is a book I found not only very rich with information about early naturalists and biologists, but also fun to read.

Hey, you might be interested in The Secret Voyage of Sir Francis Drake. The book makes a pretty good case that he did some exploring around here in 1579/80, which is 200 yrs earlier than Narváez/Vancouver/Galiano/Flores. The book is a good read, and gives a good glimpse in to the competitive world of exploration.

Trigonometry was developed for astronomy, so the history of trigonometry is more or less coextensive with the history of astronomy. I haven’t read it but this book looks promising, https://amzn.com/0195095391

Or you could try finding a book about the history of celestial navigation, something like https://amzn.com/1575240955

Or for something with a more explicit focus on trigonometry, https://amzn.com/0691175993

• • 
    
    Strogatz has a new pop math book about Calculus, Infinite Powers* https://amzn.com/dp/1328879984
    
    
• • 
    
    It’s not quite what you are asking for, but let me recommend Lockhart’s book Measurement*, https://amzn.com/dp/0674284380

Consider it as a different approach to "study harder". Pickup Infinite Powers by Steven Strogatz, and give it a read. It's a great book about the birth of calculus and how & why it's used in different applications. Perhaps this is too anecdotal, but I've gained a better appreciation for calculus and why it makes sense.

How about this: http://shatteredparadigm.blogspot.com/2008/07/amazing-video-african-man-dead-for.html

people thought the earth was flat

Not true. Most medieval people we have writings from believed the earth was a sphere including Thomas Aquinas who was in the 1200's.

http://www.amazon.com/Inventing-Flat-Earth-Columbus-Historians/dp/027595904X

I used to be a guide at the Canadian Museum of Civilization, so I can give you some basic info on the fur trade if you'd like. I checked the Museum's website for books, but it seems they don't have anything approaching the full catelogue available in the online boutique and you're probably not up for a trip here just to browse books.

Unfortunately, I don't have any particular titles that deal with Louisiana, but I can give you possible avenues for research. Torger083 already mentioned les coureurs des bois, but you should also look into the Voyageurs and the Companie des Cent Associés. Basically, the Voyageurs worked legally with the trading companies and the Coureurs des bois were basically freelancing (both groups often started families with First Nations women, leading to the eventual creation of the Métis nation). The Companie des Cent Associés was the main trading company for New France and the principle rival to the Hudson's Bay Company.

Another area to look into, of course, would be the Acadian settlers and 'la grande dérangement'--the expulsion from Nova Scotia. Many of these refugees made their way to Louisiana and became the ancestors of the Cajuns.

Indian Winter is a children's book that looks at the fur trade. It's more than a little politically incorrect by contemporary standards, but nontheless quite informative.

There's also a bit of information in First Nations--Firsthand. It's a pretty inclusive book, covering everything from first contact to modern day across North America, but necessarily skims the topics. It's also pretty euro-centric as I recall.

dum dee dum...

https://www.amazon.ca/Transylvanian-Sunrise-Radu-Cinamar-ebook/dp/B004VT144W

There is also "Transylvania Moonrise"

Did they start finding more WingMakers sites?

I've heard rumours about another site in Cuzsco Peru or something and then you have that stupid agent James Mahu talking about "Hakomi"... as in Japan?

Large Cover Up Here.

the day the earth discovered the sun was freaking amazing, and a little more grounded in reality.

http://www.amazon.com/The-Day-World-Discovered-Extraordinary/dp/0306820382/

Anything by Richard Dawkins is great for a general overview. If you wanted to drill down into human evolution, I'd recommend Last Ape Standing: The Seven-Million-Year Story of How and Why We Survived. For fun if you wanted to read an author's hypothesis on a world without humans, I'd recommend The World Without Us. Spoiler alert: cats thrive, dogs die.

The Day the World Discovered the Sun: An Extraordinary Story of Scientific Adventure and the Race to Track the Transit of Venus