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Science and Math
Science and Math World

IMPOSSIBLE! Right?You may have heard “the interior angles of a triangle always add up to 180 degrees”. This is not always true. Check out the second image, it shows a triangle with 3 right angles for a total of 270 degrees!It is true in flat

Euclideangeometry (the geometry you probably learned in school) however. But there are so many other geometries out there! You may be thinking, are other geometries real though? A mathematician would argue they are just as real as the typical flat geometry you know and love (or hate). Thesealternative geometriescan be practically useful too!The images above show triangles in spherical geometry.

Those aren’t triangles though!Oh but they are! A triangle is just a polygon enclosed by three lines. Looks like it fits the criteria.Wait but those aren’t lines, they are curved!Ah yes. I argue that these are, for all intents and purposes, just as good as lines. We need to ask: What is a line? A line is so basic to us we may not know how to describe it. I offer this definition:A line is the shortest path between 2 points.The 3 curves that make the triangle above are in fact the shortest paths from one vertex to the other on the surface of the sphere (they just so happen to be on circumferences of the sphere, which are often referred to asgreat circles). So it may be more useful to think of lines, in general, aslength minimizing curves.In conclusion, we would consider the shape above to be a triangle as it is enclosed by 3 length minimizing curves on a surface.Spherical geometry can be very useful; think about the Earth. To reduce travel time, airplanes would want to travel along great circles as they are the shortest paths from one place to another. Additionally, this type of thinking (rethinking straight lines as length minimizing curves) is central to Albert Einstein’s general theory of relativity.

read more at http://staffrm.io/@missnorledge/35H6cS1T52

“You want to do calculus with numbers? Accounting is over there, here in math we do calculus with letters.”

— Calculus professor

## who has a graphing calculator they’d like to sell me

all 3 of my kids are going into algebra-ii/trig this year. i have to buy 3.

i kinda figure there’s a bunch of you college people who no longer need yours. and i need to not spend $500 on calculators this month.

ti-83 or -84 plus would be great. color doesn’t matter, just condition.

so, if you wanna get rid of your calculator or know someone else who does, please send me a message so we can talk terms. or consider reblogging this! please!

thank you!

Probably the nerdiest thing I’ve done in some time – a math limerick of my own!

The way it should be read is:

The integral of inverse two z

Taken over a circle, size e

Divided by i

Times square root of pi

Gives you gamma of one-sixth times threeI’ve seen math limericks that used integrals before, but I haven’t seen one that would use complex analysis, so here it is

I dig it 👉🏼😎👉🏼

I have started creating these inforgraphics with different mathematical concepts. Let me know what you would like to see next. A couple of you have asked for a printable version of these, so if you are interested in printing these as posters for your class send me an email to lthmathematics@gmail.com so I can send you a pdf (easy for print).