Triangles Make All Angles

Lesson by

537

Comments 43Lesson NotesDownloads 5

Triangles Make All Angles

Lesson by

Marshall Vandruff

in The Perspective Course

537

Comments 43Lesson NotesDownloads 5

Marshall Vandruff

In this lesson, I'll break down how to use triangles to create accurate angles in 15-degree increments, covering angles from 0 to 180 degrees. I’ll demonstrate how flipping and combining simple 30/60 and 45/90 degree triangles can yield various angles, like 135, 120, 150, and even specific ones like 15 or 75 degrees. These techniques are practical for understanding angles in freehand perspective drawing without memorization, though familiarity with these increments can improve precision.

Sandra Salem

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It was interesting. Nice exercise to undust all that geometry from Elementary. I did all the angles with the triangles, adding and subtracting. To be honest I rely on this little friend at the end to make life easier. Nonetheless I am pretty confident now, that if I find myself stranded on an island I won't die for a lack of shelter. This was worth my Google search: Ecclesiastes 4:9-12. Two are better than one, because they have a good reward for their toil. For if they fall, one will lift up the other; but woe to one who is alone and falls and does not have another to help. Again, if two lie together, they keep warm; but how can one keep warm alone... 😂 By the way, your jokes are awesome! Keep working on that comedic material.

Dermot

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Marshall, that's brilliant video lesson loved it! Who would have guessed that you invented the antique monochrome test card ! The 15 degree pizza, that's my wife's portion ! Thanks :)

Christian Zinser

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Hi Marshall, great lessons so far, I'm really excited about studying perspective!! Who new that was possible... I guess I just needed to find a great teacher! I might be getting something wrong but I believe there is a mistake in the angles in the video, it skips from 105 to 130 and goes on from then. Here is a screenshot and I also attached my attempt at the angle wheel. Thanks for sharing!

Charlie Nicholson

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16h

Good catch! We'll swap it out soon!

Marshall Vandruff

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It sure does! Thank you for noticing. We got ten degrees ahead and didn't notice... then skipped only 5° at finish line. This is why we need the likes of you in this group...

Brian Slavin

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Hi Marshall, I have watched this one a few times. I’m not good at math so I need to get it through my thick skull. FYI, when you are doing the pizza analogy the 15 degree angles are off beyond the 105 degree. cheers, brian

Charlie Nicholson

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16h

Good catch! We'll swap it out soon!

Marshall Vandruff

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Indeed. Noted. We could claim it was deliberate to see if you were paying attention, but it would be a lie. It was a mistake. Thanks for pointing it out..

@jaejaelearning

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how you stacked the two triangles in the isometric video explained! Woohoo! All becomes clear in time.

Amu Noor

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Question: Are these angles used in linear perspective as well as in isometric perspective?

Marshall Vandruff

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We barely use this in Linear Perspective, but it makes sense to notice it early in training, as a foundation for how line angles can be quantified. And it's useful for sharpening your perception. It's a bit like ear training for a musician, or knowing the notes on the grand staff before improvising on an instrument.

Li Ming Lin

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I had the same question as well. I was wondering if it is for Axonometric perspective or for Linear perspective? I feel it is the latter when experimenting with some cuboids. Because Axonometric perspective is perspective without vanishing points. Then as an example, if we make the center of the circle the vanishing point, then does it become one-point perspective? Sorry if it is an obvious question :D

Donna Milligan

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Thank you! I’ve been floundering with these triangles trying to figure out what you were doing for 2 weeks. I’m also the slightest bit concerned that the course isn’t finished yet and you’re stalling for time. Hopefully not, I’m in for the whole ride no matter what. 👍

Marshall Vandruff

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Donna - the course isn't finished yet! We're producing part 2 now. If you feel like it's going too slowly, you may want to augment it by studying shading, which fits well with this one, or an unrelated subject to balance it. This is a long ride, usually with a week or two between assignments, as you apparently needed here. But it is by design that we are parsing these out...

Sarah NP

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Brilliant AND funny! Thanks Marshall.

@lucastoonz86

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I like my compass but it does damage the paper. I used 22.5 degree increments on top and 15 degree increments on bottom.

Marshall Vandruff

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You went all out. You also paid the price for the damage to the paper. Battle wounds to impress those who weren't there.

Katie

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My supernatural ability to do math only as it pertains to art is constant. I found myself having so much fun puzzling triangles together that I kept going, haha!

Marshall Vandruff

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A rare gift. And you carried it through all the way. Thanks for posting.

Randy Pontillo

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This 5 minute video taught me more about angles than the entirety of my school career

Marshall Vandruff

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Thanks Randy and Lucie. I didn't know, when we recorded it, that it would be so "for you."

Lucie VERGNON

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Same 🤣

Nassim A.

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To better understand this lesson, I tried to find on my own ways to add the 15° increments using only 45° and 60° squares. My brain melted.. But it was interesting to find out that there are several ways to get the same angles! (at least if I did it right ^^')

Marshall Vandruff

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Yay! Geometry Gamified.

John

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This was awesome, thank you Marshall. I tried using my triangles during the Isometic Optical Illusion homework assignment and was struggling in a dramatic fashion (many huffs and puffs). This was a very helpful illustration that I will practice a bunch!