Bitcoin is Vector Spaces | Abstract Algebra 37
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24
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Bitcoin is Tangents | Conics Pt 2 Ch 4
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6
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Bitcoin is the other side-angle-side inequality | Euclid's Elements Book 1 Prop 25
Assume:
- BA = ED
- AC = DF
- FE < CB
Claim: EDF < BAC
Proof method: contradiction
Suppose claim is false. Then BAC <= EDF.
Then either BAC == EDF or BAC < EDF. We proceed by falsifying both
branches.
Claim: BAC != EDF.
Proof method: contradiction.
Assume BAC == EDF. Then by side-angle-side congruence, CB = FE, which
we assumed to be false.
Claim: BAC !< EDF.
Proof method: contradiction.
Assume BAC < EDF. Then by the previous proposition, BC < EF, which we
assumed to be false.
We have eliminated both branches of EDF !< BAC. Therefore EDF < BAC.
Element page: https://mathcs.clarku.edu/~djoyce/java/elements/bookI/propI25.html
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Bitcoin is Methodology | Conics Pt 2 Ch 3
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8
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Bitcoin is the side-angle-side inequality | Euclid's Elements Book 1 Prop 24
Element page: https://mathcs.clarku.edu/~djoyce/java/elements/bookI/propI24.html
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Bitcoin is quietly reading Apollonius' own preface to Conics | Conics Pt 2 Ch 1
Types of Conics GeoGebra: https://www.geogebra.org/m/qykzuejq
Euclid Book 1 Prop 22 GeoGebra: https://www.geogebra.org/m/a7f3g6hq
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Bitcoin is how to copy an angle | Euclid's Elements Book 1 Prop 23
Element page: https://mathcs.clarku.edu/~djoyce/java/elements/bookI/propI23.html
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23
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Bitcoin is general characteristics of Apollonius' approach | Conics Pt 2 Ch 2
Cones GeoGebra: https://www.geogebra.org/m/ru6tevem
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6
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Bitcoin is fields and the SHOCKING truth about Ukraine (Artin 3.2) | Abstract Algebra 36
Craig Cannon showed up while I was reading, and we had a fascinating conversation, so I kept it in
00:00:00 Artin 3.2
00:55:00 A wild Cannon appears
00:57:00 The SHOCKING truth about Ukraine
01:01:00 What is the usual situation?
01:06:35 What is the interpretation of the SHOCKING truth?
01:15:00 What is the US military up to?
01:19:00 Is this good or bad?
01:23:55 Are private military contractors good or bad?
01:26:50 Issues with military conscription
01:28:28 The US government breaking public faith
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12
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Bitcoin is the interior triangle inequality | Euclid's Elements Book 1 Prop 21
Side argument:
BE < BA + AE
BE + EC < BA + AC
CD < CE + ED
CD + DB < CE + EB
= BE + EC
CD + DB < BA + AC
Angle argument:
CED < BDC
CEB < BAC
CED = CEB
CED < BAC
Element page: https://mathcs.clarku.edu/~djoyce/java/elements/bookI/propI21.html
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18
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Bitcoin is how to construct a triangle given 3 compatible sides | Euclid's Elements Book 1 Prop 22
Element page: https://mathcs.clarku.edu/~djoyce/java/elements/bookI/propI22.html
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3
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Skimming the Archimedes chapter | Conics Pt 1 Ch 3
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5
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The triangle inequality and Heron's problem | Euclid's Elements Book 1 Proposition 20
The correct Heron argument:
1. AE + EB' <= AP + PB' by the triangle inequality;
2. EB' = EB and PB' = PB by construction;
3. AE + EB <= AP + PB by substitution. QED.
Element GeoGebra: https://www.geogebra.org/m/mwwm78ah
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Aristaeus and Euclid | Conics Pt 1 Ch 2
Focus directrix: https://www.geogebra.org/m/rp574wzk
FQA 4: https://zxq9.com/archives/2201
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Subspaces of R^n (Artin 3.1) | Abstract Algebra 35
FQA 4: https://zxq9.com/archives/2201
FQA: https://zxq9.com/archives/category/foundations-of-qanal
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SIQA 9.5: https://rumble.com/vp5mwk-the-ladies-love-qanal-siqa-9.5.html
SIQA 10.3: https://rumble.com/vphm3w-the-founders-record-breaking-discovery-about-quaternions-siqa-10.3.html
Artin Algebra link: https://www.amazon.com/Algebra-Classic-Classics-Advanced-Mathematics/dp/0134689607/
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Discovery of the Conics | Conics Pt 1 Ch 1
00:01:15 Table of Contents
00:05:30 How to make an ellipse
00:09:08 What is a conic
00:14:00 Flat earth
00:21:25 Twitter
00:23:00 Difficult time understanding BS and reals are nulls
00:29:45 Archimedes vs. Apollonius
00:31:30 Discovery of the Conics
00:33:00 Ptolemy
00:38:40 Incidental, implicit, and accidental complexity
01:06:20 Greek math versus European math
01:21:20 Why I'm skimming
01:23:20 The point of this chapter
01:24:20 Plato was the Klaus Schwab of Ancient Greece
01:31:15 Conclusion
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zx sql nulls: https://stackoverflow.com/questions/386040/whats-wrong-with-nullable-columns-in-composite-primary-keys/16124563#16124563
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The side opposite the biggest angle is the biggest side | Euclid Elements Book 1 Prop 19
Element page: https://mathcs.clarku.edu/~djoyce/java/elements/bookI/propI19.html
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1
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Heath's Preface to Apollonius' Conics | Conics 1
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5
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The angle opposite the biggest side is always the biggest angle | Euclid Elements Book 1 Prop 18
Element page: https://mathcs.clarku.edu/~djoyce/java/elements/bookI/propI18.html
GeoGebra: https://www.geogebra.org/m/jf6kyejq
Polymathy video: https://youtu.be/Evx-3RkhtIc
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11
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Biangle Triangle Inequality | Euclid's Elements Book 1 Proposition 17
Element page: https://mathcs.clarku.edu/~djoyce/java/elements/bookI/propI17.html
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36
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Interior-Exterior Angle Inequality | Euclid's Elements Book 1 Proposition 16
Element page: https://mathcs.clarku.edu/~djoyce/java/elements/bookI/propI16.html
GeoGebra: https://www.geogebra.org/m/mwhrzheh
Euclid Elements playlist: https://odysee.com/@DoctorAjayKumar/ee
Greek Math playlist: https://odysee.com/@DoctorAjayKumar/GreekMath
Euclid Elements website: https://mathcs.clarku.edu/~djoyce/java/elements/
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Website: http://orangepill.healthcare/
6
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Vertical Angles are Congruent | Euclid Elements Book 1 Prop 15
Book 1 Prop 15: https://mathcs.clarku.edu/~djoyce/java/elements/bookI/propI15.html
Thumbnail GeoGebra: https://www.geogebra.org/m/hhqcu9ec
Euclid Elements playlist: https://odysee.com/@DoctorAjayKumar/ee
Greek Math playlist: https://odysee.com/@DoctorAjayKumar/GreekMath
Euclid Elements website: https://mathcs.clarku.edu/~djoyce/java/elements/
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8
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Converse of Prop 13 | Euclid's Elements Book 1 Proposition 14
Book 1 Proposition 14: https://mathcs.clarku.edu/~djoyce/java/elements/bookI/propI14.html
GeoGebra: https://www.geogebra.org/m/udftwvak
Euclid Elements playlist: https://odysee.com/@DoctorAjayKumar/ee
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Euclid Elements website: https://mathcs.clarku.edu/~djoyce/java/elements/
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Website: http://orangepill.healthcare/
1
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Straight Lines and Angry Dragons | Euclid's Elements Book 1 Proposition 13
Book 1 Prop 13: https://mathcs.clarku.edu/~djoyce/java/elements/bookI/propI13.html
Rational trig Scheme: https://gitlab.com/DoctorAjayKumar/wpg/-/blob/master/scm/wpg.scm
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FQA 1: https://zxq9.com/archives/2126
WildTrig: https://www.youtube.com/playlist?list=PL3C58498718451C47
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Locals: https://orangepill.locals.com/
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6
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Perps and polars | Euclid Elements Book 1 Prop 12
Geogebra B1P12: https://www.geogebra.org/m/vnb9ngry
Geogebra Pole-to-Polar: https://www.geogebra.org/m/ts6fzayw
Book 1 Prop 12: https://mathcs.clarku.edu/~djoyce/java/elements/bookI/propI12.html
Entropism article: https://zxq9.com/archives/2176
Shocking truth about determinants: https://zxq9.com/archives/2187
Foundations of QAnal: https://zxq9.com/archives/category/foundations-of-qanal
Euclid Elements website: https://mathcs.clarku.edu/~djoyce/java/elements/
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Odysee (podcast): https://odysee.com/@BigBlackCannon
Locals: https://orangepill.locals.com/
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Rumble (podcast): https://rumble.com/c/c-765395
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Website: http://orangepill.healthcare/
2
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