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Unizor | Creative Mind through Art of Mathematics
24.04.2024
Notes to a video lecture on http://www.unizor.com Trigonometry+ 08 Problem A Prove the following inequality cos(36°) ≥ tan(36°) ...
20.04.2024
Notes to a video lecture on http://www.unizor.com Trigonometry+ 07 Problem A Prove the following identity 2·arccos [ √ (1+x)/2 ] ...
17.04.2024
Notes to a video lecture on http://www.unizor.com Trigonometry+ 06 Problem A Given ∠α , ∠β and ∠γ are acute angles of a triangle....
16.04.2024
Notes to a video lecture on http://www.unizor.com Trigonometry+ 05 Problem A Given ∠α , ∠β and ∠γ are acute angles of a triangle....
07.04.2024
Notes to a video lecture on http://www.unizor.com Algebra+ 06 Problem A Prove that sum of square roots of 2 , 3 and 5 is an irrati...
03.04.2024
Notes to a video lecture on http://www.unizor.com Algebra+ 05 Problem A Given a system of two equations with three unknown variables...
25.03.2024
Notes to a video lecture on http://www.unizor.com Geometry+ 07 Problem A Given any circle with a center at point O , its diameter MN...
24.03.2024
Notes to a video lecture on http://www.unizor.com Logic+ 06 Problem A There are 5 towns. Some of them are connected by direct road...
19.03.2024
Notes to a video lecture on http://www.unizor.com Arithmetic+ 06 Problem A A positive integer number in decimal notation contains onl...
16.03.2024
Notes to a video lecture on http://www.unizor.com Logic+ 05 Problem A A casino manager, analyzing the results of operations of roule...
08.03.2024
Notes to a video lecture on http://www.unizor.com Geometry+ 06 Problem A Given an isosceles triangle Δ ABC with AB=BC and ∠ ABC=20...
05.03.2024
Notes to a video lecture on http://www.unizor.com Trigonometry+ 04 Problem A Find the sums Σ k∈[0,n−1] sin²(x+k·π/n) Solution A ...
04.03.2024
Notes to a video lecture on http://www.unizor.com Algebra+ 04 Problem A Prove that if X+Y+Z=1 then X²+Y²+Z² ≥ 1/3 . Hint A1 X² ...
03.03.2024
Notes to a video lecture on http://www.unizor.com Arithmetic+ 05 Problem A Prove that a remainder of division of any prime number P ...
26.02.2024
Notes to a video lecture on http://www.unizor.com Trigonometry+ 02 Problem A Prove the following trigonometric identities using the...
25.02.2024
Notes to a video lecture on http://www.unizor.com Trigonometry+ 03 Problem A Find the sums S sin (x,y,n)= Σ k∈[0,n] sin(x+k·y) S ...
22.02.2024
Notes to a video lecture on http://www.unizor.com Logic+ 04 Problem A A traveler has to stay in some city for 7 days. A restaurant ...
18.02.2024
Notes to a video lecture on http://www.unizor.com Arithmetic+ 04 Problem A Consider two numbers: X= 11111111 (digit 1 repeats 8 tim...
13.02.2024
Notes to a video lecture on http://www.unizor.com Logic+ 03 Problem A There are two cities: CityOfTruth, where all people always te...
12.02.2024
Notes to a video lecture on http://www.unizor.com Algebra+ 03 Problem A Let n be any natural number/ Define two functions of n : ...
05.02.2024
Notes to a video lecture on http://www.unizor.com Geometry+ 05 Problem A Construct a quadrilateral ABCD by its 4 sides AB , BC , C...
29.01.2024
Notes to a video lecture on http://www.unizor.com Geometry+ GeoTheorem 1 Theorem Prove that non-null vector n ( a,b,c ) in three-di...
28.01.2024
Notes to a video lecture on http://www.unizor.com Geometry+ 04 This lecture is dedicated to planes, straight lines and their perpendi...
24.01.2024
Notes to a video lecture on http://www.unizor.com Geometry+ 03 This lecture is dedicated to problems of triangle construction by its ...
23.01.2024
Notes to a video lecture on http://www.unizor.com Geometry+ 02 This lecture is dedicated to problems of triangle construction by its ...
21.01.2024
Notes to a video lecture on http://www.unizor.com Trigonometry+ 01 Problem A Using the Euler Formula e i·x = cos(x)+i·sin(x) pro...
18.01.2024
Notes to a video lecture on http://www.unizor.com Arithmetic+ 03 Problem A I have purchased a share of some company XYZ for price P...
12.01.2024
Notes to a video lecture on http://www.unizor.com Algebra+ 02 Problem Let { x i } (where i ∈[ 1,n ] and n is any natural number) b...
10.01.2024
Notes to a video lecture on http://www.unizor.com Algebra+ 01 Problem A Given an equation of parabola in Cartesian coordinates on a...
07.01.2024
Notes to a video lecture on http://www.unizor.com Geometry+ 01 Problem A Can two sides and all angles of one triangle be equal to tw...
24.12.2023
Notes to a video lecture on http://www.unizor.com Logic 02 Problem A The game starts with two sets of stones and two players. At ea...
10.12.2023
Notes to a video lecture on http://www.unizor.com Arithmetic 02 Problem Prove that S N = Σ n∈[2,N] 1/n is not an integer number ...
07.12.2023
Notes to a video lecture on http://www.unizor.com Arithmetic 01 Problem A Given n pieces of rope. Some of them are cut into n sm...
06.12.2023
Notes to a video lecture on http://www.unizor.com Logic 01 Problem A Given a rectangular matrix with m rows and n columns. It's f...
04.12.2023
Notes to a video lecture on http://www.unizor.com Who Needs Problems? Nobody. Nobody needs problems. People need solutions. But ho...
29.11.2023
Notes to a video lecture on UNIZOR.COM Newton + Maxwell = m·c² In this lecture we will use the laws of classic Newtonian mechanics and ...
18.11.2023
Notes to a video lecture on http://www.unizor.com Momentum of Light In this lecture we will deal with electromagnetic field in vacuum w...
06.11.2023
Notes to a video lecture on http://www.unizor.com Electromagnetic Energy Flux Density As we have established earlier (lectures Electri...
22.10.2023
Notes to a video lecture on http://www.unizor.com Electromagnetic Energy Continuity Let us recall the definition of the divergence of ...
16.10.2023
Notes to a video lecture on http://www.unizor.com Electromagnetic Waves Amplitude In the previous lecture Speed of Light of the curren...