WildTrig3: Spread, angles and astronomy

Angles have their origin in astronomy and spherical trigonometry. Here we introduce the rational alternative, called spread, and give examples from ISO paper sizes to the faces of a dodecahedron.

Category:

Science & Technology

Tags:

• rational
• trigonometry
• angle
• spread
• quadrance
• mathematics
• dodecahedron
• tetrahedron

[footstep002]

Hello, Prof. Wildberger. Thanks for your quick answer.

I have another question. You said spread are all same in four sides because it is defined to be between lines. But I still don't understand. So what you are saying is that no matter what spread side you mark with, the narrower side's spread is always is the defined one?

Then how do you define the wider one?

To me even if spread is all about between the lines, wider one seems different if you define from that side of the lines.

[njwildberger]

@footstep002 It is not so elementary to discuss the four regions formed by two intersecting lines. However later in this series I discuss the Triangle Spread Rules, which distinguish between convex obtuse and acute sectors of a triangle (it is really in the context of a triangle that this distinction is most valuable). For now, just try to get used to the idea that spread is between lines, not associated with any wider or narrower sides.

[footstep002]

In the video at 4:30 there's a illustration about spreads in four sides, that are equal. I get that oppsite side spread is same. What I don't get is that spread between quadrance R and P is equal to the spreads that are adjacent(the wider one).

Please explain why they are same.

[njwildberger]

@footstep002 In rational trigonometry, the spread is defined between lines, not rays.

[hanko2001]

Is the scale on a spread protractor logarithmic? I only discovered your videos because I made some videos with tags "polar trigonometry" and one of your videos came up as a related video.

[njwildberger]

Hi, No the scale is not logarithmic. If you google `rational trigonometry protractor' you will find a very pleasant one (actually several) created by Michael Ossmann that you can download.

[MrTanookiMario]

@footstep002

In more conventional terms, it's exactly the same reason that you'd get identical solutions to sin(45°) and sin(135°) (or any other such pairs that sum to 180°).

Spread isn't the same thing as angle; it's about ratios--not "width."

[nfwu]

@isilder The entire point of this series of videos (as I understand it) is to completely avoid invoking transcendental functions. i.e.: trigonometry without requiring calculators/trig tables because sine, cosine and tangent are simply unnecessary.

[TheBooTya]

@isilder

spread is actually a sin squared. anyway, it is just another way of seeing things.

[isilder]

More propaganda.. spread is just sine(angle), so we really see that you are just copyring trigonometry with just some bare faced propaganda..

eg There is nothing wrong with infinity as the ratio for parallel (conicident for gap=0) lines... your spread also does not convey the distance between parallel lines..so parallel lines are rules out from spread, and yet you used it to argue against using ratios and angles ! You did no better but just claimed it was better ..only through a smokescreen .