When he puts the triangles into the circle, there is still a space between the base of each triangle and the outside of the circle (which he points out). Then, he bases the whole equation on the fact that the base of the triangle is the circumference of the circle. But they are NOT equal! The base of the triangle should be less than the circumference. What am I missing? (around 2:15 )

They are not equal. The height of the triangle is slightly less than R due to the missing section and you can't stack the triangle up next to each other to form a bigger triangle, that assumption doesn't work . In his example the hypotenuse is longer than R so it can't be one of the triangles from the circle.

Wait earlier in the video, didn't he say that 0.9 recurring and 1 were equal on the real numberline, because there wasn't any real number to represent the change difference(which was a infinitesimal), but 0.9 repeating and 1 were actually different and unequal. He then proceeds to say, later in the video, infinitesimals explain why 0.9 repeating equals 1...

all you have to do is round up from 0.9 to 1 whole because if it is below 0.5 well technially below 0.4 you will round down and if it is above 0.5 then it add's up to a whole.explain by a future professor.

Main content

Course: Breakthrough Junior Challenge > Unit 1

Lesson 1: 2015 Challenge — Mathematics

Infinitesimals and non-standard analysis

Google Classroom

By Shaun Regenbaum

This video intuitively explains infinitesimals and the basics of Non-Standard Analysis. There are simplifications of advanced mathematics, just beware. Thanks to DM Ashura (Bill Shillito) for his awesome music and his constant support for my love of math and science. He is truly an inspiration.

Want to join the conversation?

Sort by:

always.writes
Posted 8 years ago. Direct link to always.writes's post “When he puts the triangle...”
When he puts the triangles into the circle, there is still a space between the base of each triangle and the outside of the circle (which he points out). Then, he bases the whole equation on the fact that the base of the triangle is the circumference of the circle. But they are NOT equal! The base of the triangle should be less than the circumference. What am I missing? (around
2:15
)
Button navigates to signup pageButton navigates to signup page
(6 votes)
Answer
- William Taggart
  Posted 8 years ago. Direct link to William Taggart's post “They are not equal. The h...”
  They are not equal. The height of the triangle is slightly less than R due to the missing section and you can't stack the triangle up next to each other to form a bigger triangle, that assumption doesn't work . In his example the hypotenuse is longer than R so it can't be one of the triangles from the circle.
  Button navigates to signup page
  (6 votes)
Nat
Posted 8 years ago. Direct link to Nat's post “At around 2:48, I don't u...”
At around
2:48
, I don't understand how the base of the final triangle would be the circumference of the circle. I mean, the base of each small triangle is not equal to the curvy bit underneath it (since a curved line reaching from point a to be would be bigger than a straight one going from a to b), meaning that if you add all the triangle bases together, they would not equal the circumference. I'm probably wrong but I just don't get it. Can anyone explain it?
Button navigates to signup pageButton navigates to signup page
(4 votes)
Answer
Monish Jampala
Posted 8 years ago. Direct link to Monish Jampala's post “What is the Zorn's Lemma ...”
What is the Zorn's Lemma and what are ultrafilters
Button navigates to signup pageButton navigates to signup page
(3 votes)
Answer
Ming315
Posted 4 years ago. Direct link to Ming315's post “Wait earlier in the video...”
Wait earlier in the video, didn't he say that 0.9 recurring and 1 were equal on the real numberline, because there wasn't any real number to represent the change difference(which was a infinitesimal), but 0.9 repeating and 1 were actually different and unequal. He then proceeds to say, later in the video, infinitesimals explain why 0.9 repeating equals 1...
Button navigates to signup pageComment on Ming315's post “Wait earlier in the video...”
(2 votes)
Answer
- rubentaten
  Posted 3 years ago. Direct link to rubentaten's post “all you have to do is rou...”
  all you have to do is round up from 0.9 to 1 whole because if it is below 0.5 well technially below 0.4 you will round down and if it is above 0.5 then it add's up to a whole.explain by a future professor.
  Button navigates to signup page
  (2 votes)
Arthur Dent
Posted 8 years ago. Direct link to Arthur Dent's post “If you ask Vi Hart, they ...”
If you ask Vi Hart, they are the same... Why Am I SO CONFUSED??
Button navigates to signup pageButton navigates to signup page
(2 votes)
Answer
Destroyer 74
Posted 8 years ago. Direct link to Destroyer 74's post “What exactly is an epsilo...”
What exactly is an epsilon?
Button navigates to signup pageButton navigates to signup page
(1 vote)
Answer
Kabya Roy
Posted 6 years ago. Direct link to Kabya Roy's post “What are infinitesimals a...”
What are infinitesimals actually?
Button navigates to signup pageButton navigates to signup page
(1 vote)
Answer
abedin
Posted 4 years ago. Direct link to abedin's post “Hey, this is Sango the qu...”
Hey, this is Sango the question is How am I going to get this scholarship like by doing what thing?
Button navigates to signup pageComment on abedin's post “Hey, this is Sango the qu...”
(0 votes)
Answer

Breakthrough Junior Challenge

Course: Breakthrough Junior Challenge > Unit 1

Want to join the conversation?

Video transcript