18.319, Fall 2005.
Problem Set 2
Instructions: Solve your favourite problems from the list below. Open problems are marked
with ; hard (but feasible) problems are marked with .
1. Let a(P ) denote the number of angles determined by ordered triples of a
18.319, Fall 2005.
Problem Set 1
Instructions: Solve your favourite problems from the list below. Open problems are marked
with ; hard (but feasible) problems are marked with .
1. Find all planar p oint congurations with n points that determine exactly
18.319, Fall 2005.
Problem Set 4
Problems from Matoueks textbook on Discrete Geometry are marked with ; hard (but
s
feasible) problems are marked with .
1. (a) Prove that the maximum length of the Davenport-Schinzel sequence of order 2 over
an alphabet o
18.319, Fall 2005.
Problem Set 3
Instructions: Solve your favourite problems from the list below. Open problems are marked
with ; hard (but feasible) problems are marked with .
1. (Szkely, 1997) For a simple graph G and k N, let kG denote the graph obtain
18.319, Fall 2005.
Problem Set 6
Open problems are marked with ; hard (but feasible) problems are marked with .
1. (Radon, 1952) Every set of d + 2 points in Rd can be partitioned into two subsets such
that their convex hulls intersect.
2. (Las Vergnas &
18.319, Fall 2005.
Problem Set 5
Open problems are marked with ; hard (but feasible) problems are marked with .
Problems from Matoueks textbook on Discrete Geometry are marked with .
s
1. (Asano et al., 1999) You are given a nite set S of pairwise disjoi
BARCELONA, Spain Stephen Curry made six 3-pointers and scored 20 points, leading the U.S. national team into the
quarterfinals of the Basketball World Cup with an 86-63 victory over Mexico on Saturday.
The Golden State Warriors All-Star was 7 of 10 from t
SW COMPOUND/REVERSED CURVE
1. A compound curve has the following
data: I1 = 28, I2 = 31, D1 = 3, D2 =
4, and Sta PI = 30+120.5. Find all the
elements of the reversed curve including
2. A compound curve has the following
properties: I1 = 32 Length of long